1.

2.

Student: Kiare Mays Date: 06/15/20

Instructor: Valery Shemetov Course: MTH154 – Quantitative Reasoning (with MCR4)

Assignment: Section 6.2 Homework

Given the exponential equation , complete parts (a) through (b) below.y = 250 • e 0.0845 • x

(a) Represent as a decimal to 4 decimal places.e 0.0845

(Round to four decimal places as needed.)

(b) Rewrite the equation in the form .P = P • (1 + r)0 x

P = 250 • (1.0845)x

P = 250 • (1 + 8.82%)x

P = 250 • (0.0882)x

P = 250 • (1 + 8.45%)x

A population can be modeled by the exponential equation , where t years since 1990 and y population. Complete parts (a) through (d) below.

y = 250,000 • e − 0.0757 • t = =

(a) What is the continuous decay rate per year? (Hint: If the rate k is a negative number, this implies a continuous decay rate with the opposite sign of k.)

The population is decreasing at a continuous rate of % per year. (Round to two decimal places as needed.)

(b) What is the annual decay rate (not continuous)? (Hint: If the rate r is a negative number, this implies an annual decay rate with the opposite sign of r.)

The population is decreasing at an annual rate of % per year. (Round to two decimal places as needed.)

(c) Rewrite the equation in the form .P = P • (1 + r)0 t

A. P = 250,000 • (1 − 7.57%)t

B. P = 250,000 • (0.9243)t

C. P = 250,000 • ( − 0.729)t

D. P = 250,000 • (0.9271)t

(d) How many people will there be after 8 years?

people (Round to the nearest whole number as needed.)

3. A population can be modeled by the exponential equation , where t years since 2010 and y population. Complete parts (a) through (d) below.

y = 11,000 • e 0.2124 • t = =

(a) What is the continuous growth rate per year?

% (Round to two decimal places as needed.)

(b) What is the annual growth rate (not continuous)?

% (Round to two decimal places as needed.)

(c) Rewrite the equation in the form .P = P • (1 + r)0 t

A. P = 11,000 • (1.2124)t

B. P = 11,000 • (0.2366)t

C. P = 11,000 • (1 + 21.24%)t

D. P = 11,000 • (1 + 23.66%)t

(d) How many people will there be after 8 years?

people (Round to the nearest whole number as needed.)

4. Consider the following case of exponential growth. Complete parts a through c below.

The population of a town with an initial population of grows at a rate of % per year.48,000 7.5

a. Create an exponential function of the form , (where r 0 for growth and r 0 for decay) to model the situation described.

Q = Q (1 + r)0 × t > <

Q ( )= × t

(Type integers or decimals.)

b. Create a table showing the value of the quantity Q for the first 10 years of growth.

Year t= Population Year t= Population 0 48,000 6 1 7 2 8 3 9 4 10 5

(Round to the nearest whole number as needed.)

c. Make a graph of the exponential function. Choose the correct graph below.

A.

0 10 40,000

110,000

Year

Po pu

la tio

n

B.

0 10 30,000

100,000

Year

Po pu

la tio

n

C.

0 10 40,000

100,000

Year

Po pu

la tio

n

D.

0 10 20,000

100,000

Year

Po pu

la tio

n

5. Consider the following case of exponential decay. Complete parts (a) through (c) below.

A privately owned forest that had acres of old growth is being clear cut at a rate of % per year.5,000,000 2

a. Create an exponential function of the form , (where r 0 for growth and r 0 for decay) to model the situation described.

Q = Q (1 + r)0 × t > <

Q ( )= × t

(Type integers or decimals.)

b. Create a table showing the value of the quantity Q for the first 10 years of growth.

Year t= Acres Year t= Acres 0 5,000,000 6 1 7 2 8 3 9 4 10 5

(Round to the nearest whole number as needed.)

c. Make a graph of the exponential function. Choose the correct graph below.

A.

0 10 4,000,000

5,000,000

Year

Ac re

s

B.

0 10 0

1,000,000

Year

Ac re

s

C.

0 10 4,000,000

5,000,000

Year

Ac re

s

D.

0 10 4,000,000

5,000,000

Year

Ac re

s

6. Answer the questions for the problem given below. The average price of a home in a town was $ in 2007 but home prices are rising by % per year.179,000 3

a. Find an exponential function of the form (where r 0) for growth to model the situation described.Q = Q (1 + r)0 × t >

Q $ (1 )= × + t

(Type an integer or a decimal.)

b. Fill the table showing the value of the average price of a home for the following five years.

Year t= Average price 0 $179,000 1 $ 2 $ 3 $ 4 $ 5 $

(Do not round until the final answer. Then round to the nearest dollar as needed.)

7. Consider the following case of exponential growth. Complete parts (a) through (c) below.

Your starting salary at a new job is $ per month, and you get annual raises of % per year.1700 6

a. Create an exponential function of the form , (where r 0 for growth and r 0 for decay) to model the monthly salary situation described.

Q = Q (1 + r)0 × t > <

Q ( )= × t

(Type integers or decimals.)

b. Create a table showing the value of the quantity Q for the first 10 years of growth.

Year t= Salary (per month) Year t= Salary (per month) 0 $1700 6 $ 1 $ 7 $ 2 $ 8 $ 3 $ 9 $ 4 $ 10 $ 5 $

(Round to two decimal places as needed.)

c. Make a graph of the exponential function. Choose the correct graph below.

A.

0 10 0

800 1,600 2,400 3,200 4,000

Year

Sa la

ry (d

ol la

rs ) B.

0 10 0

800 1,600 2,400 3,200 4,000

Year

Sa la

ry (d

ol la

rs )

C.

0 10 0

800 1,600 2,400 3,200 4,000

Year

Sa la

ry (d

ol la

rs ) D.

0 10 0

800 1,600 2,400 3,200 4,000

Year

Sa la

ry (d

ol la

rs )

8.

9.

Air pressure can be modeled by the exponential equation , where x altitude in 1000's of feet and y air pressure in psi. Complete parts (a) through (e) below.

y = 14.1 • e − 0.0423 • x = =

(a) What is the continuous decay rate per 1000 feet? (Hint: If the rate k is a negative number, this implies a continuous decay rate with the opposite sign of k.)

The air pressure is decreasing at a continuous rate of % per 1000 feet. (Round to two decimal places as needed.)

(b) What is the decay rate every 1000 feet (not continuous)? (Hint: If the rate r is a negative number, this implies an annual decay rate with the opposite sign of r.)

The air pressure is decreasing at a rate of % per 1000 feet. (Round to two decimal places as needed.)

(c) Rewrite the equation in the form .P = P • (1 + r)0 x

A. P = 14.1 • (0.9586)x

B. P = 14.1 • (1.0414)x

C. P = 14.1 • (1 − 4.23%)x

D. P = 14.1 • (0.9577)x

(d) What is the air pressure at 35,000 feet?

psi (Round to two decimal places as needed.)

(e) What is the air pressure at sea level?

psi (Round to one decimal place as needed.)

You can not print this question until you complete the required media.

Written Case #2

THE TEAM MEMBER FROM HELL

(Part A) – Mike’s Perspective

Let me tell you about my teammate from hell. Someone with no motivation to succeed is the

worst kind of member to have in a group because it is nearly impossible to motivate him to do

the work and perform it well. It was apparent from the beginning John had no motivation. After

our group was already formed by the teacher, a late comer came to class and the teacher assigned

him to our group. His name was John. Already I was a little weary, the students who come to

class a couple of days after it begins are the slackers, they were either skipping the first days or

they didn't have their schedule together.

At our first meeting my expectations were met. I found out John is a member of a fraternity and

he did nothing but talk about his social life. I must say though, John was entertaining. He could

make us laugh, mainly because he didn't seem to know what he was talking about.

Unfortunately, John could also be loud and obnoxious and often his jokes were simply not funny.

He just did not understand the difference between social hour and work life.

Although John plans on working in his family's business when he graduates, he was working 20-

30 hours a week for spending money and to help pay tuition. I don't think he wanted to be in

school and might have dropped out if it weren't for all his friends. John seemed like someone you

would always have to push a little harder to get anything done. He made no attempt to discuss

anything about the project or even discuss his life around academics. It was only about partying.

We discussed what we would prepare for our next meeting. John did not volunteer his services

for any of the tasks and when we assigned him one he seemed very annoyed and unsatisfied. At

the next meeting John showed up late and was unprepared. I was disappointed. It wasn't the end

of the world but I couldn't help but look ahead at the complex project we were to complete. If

this is the attitude and work ethic he brings to the table at the second meeting, how are we ever

going to get a solid project completed? I have a dream to make something of myself when I

graduate so I am concerned with my grades and don't want to be dragged down by someone who

doesn't care. I would almost rather do things on my own.

We decided that the workload would be distributed evenly among all members of the group.

Each member of the group chose a certain activity to fulfill. The workload was evenly

distributed and the members of the group all began to work towards completing their selected

work. Things seemed to be going well until another group member and I realized that John was

not completing his required work. He had an attitude about school that was not very positive and

was not doing well in the class. We tried to motivate him by explaining that if we successfully

completed the project he would successfully complete the course. This seemed to work initially

but we soon learned he was still not completing the work. We discussed the situation and

offered to help him if he was having difficulties. Again this worked temporarily but he fell back

into the same pattern.

It wasn't as though the group didn't make an effort to get him involved. Two of us kept reminding

him to do his part of the project. He'd smile and give a little chuckle. We also sent numerous e-

mails to him practically begging him to attend the meetings so that we could have his input, as

well as save his grade. He never responded to the messages. At the meetings he did show up to I

confronted him and asked if he would make more of a consistent effort to attend group meetings.

He was really laid back and would always just tell us that he was busy and would do what he

could. Eventually one of the members blew up at him. She told him that he was being

disrespectful and that if he didn't want to do anything that he shouldn't show up. After that the

only thing he changed was that he came to meetings but was quiet and still did almost no work.

He just walked in, sat there while we did work and then took credit for work that he did not do.

As time went on we noticed John was trying to make small attempts to slowly work his way back

into the group. I think he began to notice what a good time we were having working together to

complete the project. As he became more vocal and offered some opinions, we really didn't want

to listen to what he had to say. We were far along with the project and didn't need his input at

2

this time. Also, we no longer trusted him and did not feel that we could rely on him. I didn't take

anything he said seriously and when he offered to do something I didn't expect him to do it. He

began to complain and make sarcastic responses such as "oh I guess nobody hears me."

As the project deadline grew near, we agreed that we must meet early in the week and then at the

end of the week and then over the weekend one final time. However, after thinking about the

current plans just made, John realized his fraternity's semi-formal was that same weekend and he

claimed there was no time over the weekend that he could work on the project. This statement got

me thinking. Does he expect the rest of us to finish the project for him? Does he really have the

nerve to change our plans just so he can get drunk all weekend? What are his priorities, school or

partying? Suddenly, after this occurred I felt tremendous pressure. Not only do I and my other

teammates have to orchestrate everything to finish the project, but we are the only ones who care

about the quality of our work too. We could have talked to him again about his performance but

we never did. We just wanted to get the work done and go home as soon as we could.

I finally called our Professor and asked her if we could remove John from our group. She wants

to meet with all of us on Tuesday.

THE TEAM MEMBER FROM HELL

(Part B) John’s Perspective

Let me tell you about a team member from hell. I was in a group with Mike, who likes to have

things done his way without help from anyone, which I knew was going to be a problem.

The group assignment consisted of answering fifty multiple choice questions that covered what

we had learned throughout the semester. At our first group meeting Mike didn't want to waste

time getting to know the members of the group. Not only did he not allow himself to get to

know these people, he didn't allow the remaining members to get to know each other because it

would be a waste of time. Instead of "wasting time going through every problem together as a

group," as he put it, he delegated certain questions to each member. He decided that each

member would do his or her assigned part and we would all meet a half hour before the next

3

class to exchange answers. He decided that, as a group, we could discuss any problems we had

with particular questions in that allotted time.

Mike did not want to hear any rationale about how this plan could go terribly wrong. His

stubbornness made it impossible to get any other ideas through. My complaints went ignored

and he took his "leader" role, which felt more like a dictatorship. He had to be in control;

whatever I said was wrong and what he said was right. He would not listen. When I said

something, he would not even acknowledge me. I felt many of his ideas were bad but I didn't say

anything because I did not want to start an argument. Although he wanted things to be done his

way, he didn't want to spend a lot of time doing them. He was not organized either. Instead of

finishing one job first, he would jump all around and have more than one project going. This

made the group more stressful. I hated attending the meetings. I could tell others felt the same

way. At one point I stopped going to the meetings, but my group members begged me to attend.

Our Professor knows we are having problems and has asked to meet with all of us on Tuesday.

Assignment

In the meeting with the Professor on Tuesday, the group finds out that the Professors have

worked it out so that all groups in the class will be working together in the same teams next

semester as well. This is so that the teams have to address their problems rather than ignore them.

The Professor offered to have a former student of hers work with Mike and John’s team as a

consultant – to help them work through their problems. Everyone in the group agreed that this

would be a great idea.

You are the former student who will be consulting with this team. What will you do?

Possible theories to apply: Personality theories; attribution theory (for example, the fundamental

attribution error and self-serving bias); perception and the strategies your book lists for reducing

perceptual biases; all of the motivation theories we covered (how might the group work to

motivate John); theories or ideas about group dynamics and team effectiveness such as social

loafing, facilitation, stages of group development, and what it says about setting up a team for

success (process losses – and when there is a process loss, what should be examined).

4

1.

2.

3.

Student: Kiare Mays Date: 06/15/20

Instructor: Valery Shemetov Course: MTH154 – Quantitative Reasoning (with MCR4)

Assignment: Section 6.1 Homework

You deposit $ into a savings account with an APR of %. Complete parts (a) through (c) below.4000 5.7

(a) Compute the amount of interest you gain after 1 year.

$ (Round to the nearest dollar as needed.)

(b) To compute the amount of money in the savings account at the end of 1 year, take the original value and add interest: . This is equivalent to multiplying $ by what factor?$4000 + 5.7% • $4000 4000

(Round to three decimal places as needed.)

(c) Fill in the following table, one year at a time:

(Round to the nearest cent as needed.) Year Beginning Interest End 1 $4000 $ $ 2 $ $ $ 3 $ $ $ 4 $ $ $ 5 $ $ $

Calculate the amount of money you'll have at the end of the indicated time period, assuming that you earn simple interest.

You deposit $ in an account with an annual interest of % for years.3900 3.2 5

The amount of money you'll have at the end of years is $ .5 (Type an integer or a decimal.)

Complete the table, for the following investments, which shows the performance (interest and balance) over a 5-year period.

Suzanne deposits $ in an account that earns simple interest at an annual rate of %. Derek deposits $ in an account that earns compound interest at an annual rate of % and is compounded annually.

4000 4.4 4000

4.4

Year Suzanne's

Annual Interest

Suzanne's Balance

Derek's Annual Interest

Derek's Balance

1 $____ $____ $____ $____ 2 $____ $____ $____ $____ 3 $____ $____ $____ $____ 4 $____ $____ $____ $____ 5 $____ $____ $____ $____

Complete the following table.

(Round to the nearest dollar as needed.)

Year Suzanne's Annual Interest Suzanne's

Balance Derek's Annual

Interest Derek's Balance

1 $ $ $ $

2 $ $ $ $

3 $ $ $ $

4 $ $ $ $

5 $ $ $ $

4.

5.

6.

7.

Use the compound interest formula to determine the accumulated balance after the stated period.

$ invested at an APR of % for years.6000 5 2

If interest is compounded annually, what is the amount of money after years?2

$ (Do not round until the final answer. Then round to the nearest cent as needed.)

Use the compound interest formula to compute the balance in the following account after the stated period of time, assuming interest is compounded annually.

$ invested at an APR of % for years.7000 4.2 21

The balance in the account after years is $ .21 (Round to the nearest cent as needed.)

You deposit $ into a savings account with an APR of %. Complete parts (a) through (c) below.3500 1.4

(a) Compute the amount of interest you gain after 1 year.

$ (Round to the nearest dollar as needed.)

(b) To compute the amount of money in the savings account at the end of 1 year, take the original value and add interest: . This is equivalent to multiplying $ by what factor?$3500 + 1.4% • $3500 3500

(Round to three decimal places as needed.)

(c) To compute the amount of money in the account after 6 years you would multiply $ by what factor?3500

(Round to three decimal places as needed.)

You deposit $ into a savings account with an APR of %. Use the table to complete parts (a) through (b) below.350 3.3

A B 1 Year Amount 2 0 $350 3 1 $361.55 4 2 $373.48 5 3 $385.81 6 4 $398.54

(a) What recursive formula would you enter in cell B3 that could be filled down?

B2= * 0.033

B$2= * 1.033

B2= * 1.033

B$2 ^A3= * 1.033

(b) What closed formula would you enter in cell B3 that could be filled down?

B$2 ^A$3= * 1.033

B$2= * 0.033

B$2= * 1.033

B$2 ^A3= * 1.033

8.

9.

10.

11.

12.

Describe the basic differences between linear growth and exponential growth.

Choose the correct answer below.

A. Linear growth occurs when a quantity grows by different, but proportional amounts, in each unit of time, and exponential growth occurs when a quantity grows by random amounts in each unit of time.

B. Linear growth occurs when a quantity grows by the same relative amount, that is, by the same percentage, in each unit of time, and exponential growth occurs when a quantity grows by the same absolute amount in each unit of time.

C. Linear growth occurs when a quantity grows by the same absolute amount in each unit of time, and exponential growth occurs when a quantity grows by the same relative amount, that is, by the same percentage, in each unit of time.

D. Linear growth occurs when a quantity grows by random amounts in each unit of time, and exponential growth occurs when a quantity grows by different, but proportional amounts, in each unit of time.

The population of a town is increasing by people per year. State whether this growth is linear or exponential. If the population is today, what will the population be in years?

639 1800 five

Is the population growth linear or exponential?

exponential

linear

What will the population be in years?five

The price of a computer component is decreasing at a rate of % per year. State whether this decrease is linear or exponential. If the component costs $ today, what will it cost in three years?

10 120

Is the decline in price linear or exponential?

linear

exponential

What will the component cost in three years? $ (Round to the nearest cent as needed.)

You can not print this question until you complete the required media.

You can not print this question until you complete the required media.

1.

2.

Student: Kiare Mays Date: 06/15/20

Instructor: Valery Shemetov Course: MTH154 – Quantitative Reasoning (with MCR4)

Assignment: Section 6.3 Homework

Your mutual fund goes up % in the first year, then down % in the 2nd year, and finally up again % in the 3rd year. Complete parts a and b.

12.3 2.1 5.6

a) What is the average rate of return per year?

% (Do not round until the final answer. Then round to two decimal places as needed.)

b) If the fund plummets % in the 4th year, what is the average rate of return per year for the 4 years?31

% (Do not round until the final answer. Then round to two decimal places as needed.)

You average mph for the first miles of a trip and then mph for the next miles. Complete parts a and b.44 20 55 20

a) What is the average speed over the miles?40

mph (Type an integer or a decimal rounded to one decimal place.)

b)  If you then average mph over the next miles what is the average speed over the miles?75 20 60

mph (Type an integer or a decimal rounded to one decimal place.)

3.

4.

5.

1: Types of means.

(1) arithmetic geometric harmonic

(2) arithmetic geometric harmonic

Determine whether to use the arithmetic mean, the geometric mean, or the harmonic mean to complete parts a and b.

Click the icon to view the three types of means.1

a) You mix equal weights of ( kg/ ), ( kg/ ), and ( kg/ ) together. What is the density of the resulting alloy? (Hint: Density is the rate of weight to volume, kg/ .)

Gold 19,320 m3 Europium 5243 m3 Aluminum 2712 m3

m3

To find the density of the resulting alloy, the (1) mean should be used and the density is

kg/ .m3

(Type an integer or a decimal rounded to one decimal place.)

b)  If your veggie hot dog stand generates revenues of $ , $ , and $ at 3 events, what is your average revenue per event?

19,320 5243 2712

To find the average revenue per event, the (2) mean should be used and the average revenue is $ . (Round to the nearest cent as needed.)

The arithmetic mean, , is an average of n numbers. a1 + a2 +⋯ + an

n

The geometric mean, , is the average of change in growth where the rate of growth and/or decay changes over time.

n a1 • a2 •⋯ • an

The harmonic mean, , is the average of rates, as in travelling n miles at one rate and n miles at

another rate.

n 1

a1 +

1 a2

+⋯ + 1

an

Suppose the rate of return for a particular stock during the past two years was % and %. Compute the geometric mean rate of return. (Note: A rate of return of % is recorded as , and a rate of return of % is recorded as .)

5 35 5 0.05 35 0.35

The geometric mean rate of return is %. (Round to one decimal place as needed.)

Suppose the rate of return for a particular stock during the past two years was % and . Compute the geometric mean rate of return.

10 − 40%

The geometric mean rate of return is %. (Round to one decimal place as needed.)

6.

7.

(1) more less

A company's stock price rose % in 2011, and in 2012, it increased %.1.7 17.1

a. Compute the geometric mean rate of return for the two-year period 2011 2012. (Hint: Denote an increase of % by .)

− 17.1 0.171

b. If someone purchased $1,000 of the company's stock at the start of 2011, what was its value at the end of 2012? c. Over the same period, another company had a geometric mean rate of return of %. If someone purchased $1,000

of the other company's stock, how would its value compare to the value found in part (b)? 32.11

a. The geometric mean rate of return for the two-year period 2011 2012 was %.− (Type an integer or decimal rounded to two decimal places as needed.)

b. If someone purchased $1,000 of the company's stock at the start of 2011, its value at the end of 2012 was $ . (Round to the nearest cent as needed.)

c. If someone purchased $1,000 of the other company's stock at the start of 2011, its value at the end of 2012 was

$ , which is (1) than the value from part (b). (Round to the nearest cent as needed.)

(1) more less

A company's stock price rose % in 2011, and in 2012, it increased %.3.9 75.8

a. Compute the geometric mean rate of return for the two-year period 2011 2012. (Hint: Denote an increase of % by .)

− 75.8 0.758

b. If someone purchased $1,000 of the company's stock at the start of 2011, what was its value at the end of 2012? c. Over the same period, another company had a geometric mean rate of return of %. If someone purchased $1,000 of

the other company's stock, how would its value compare to the value found in part (b)? 10.3

a. The geometric mean rate of return for the two-year period 2011 2012 was %.− (Type an integer or decimal rounded to two decimal places as needed.)

b. If someone purchased $1,000 of the company's stock at the start of 2011, its value at the end of 2012 was $ . (Round to the nearest cent as needed.)

c. If someone purchased $1,000 of the other company's stock at the start of 2011, its value at the end of 2012 was

$ , which is (1) than the value from part (b). (Round to the nearest cent as needed.)

8.

2: Data table for total rate of return

3: Geometric mean rate of return for stock market indices

The data in the accompanying table represent the total rates of return (in percentages) for three stock exchanges over the four-year period from 2009 to 2012. Calculate the geometric mean rate of return for each of the three stock exchanges.

Click the icon to view data table for total rate of return for stock market indices.2 Click the icon to view data table for total rate of return for platinum, gold, and silver.3

a. Compute the geometric mean rate of return per year for the stock indices from 2009 through 2012.

For stock exchange A, the geometric mean rate of return for the four-year period 2009-2012 was %. (Type an integer or decimal rounded to two decimal places as needed.)

For stock exchange B, the geometric mean rate of return for the four-year period 2009-2012 was %. (Type an integer or decimal rounded to two decimal places as needed.)

For stock exchange C, the geometric mean rate of return for the four-year period 2009-2012 was %. (Type an integer or decimal rounded to two decimal places as needed.)

b. What conclusions can you reach concerning the geometric mean rates of return per year of the three market indices?

A. Stock exchange B had a higher return than exchange C and a much higher return than exchange A.

B. Stock exchange C had a much higher return than exchanges A or B. C. Stock exchange A had a much higher return than exchanges B or C. D. Stock exchange A had a higher return than exchange C and a much higher return than

exchange B.

c. Compare the results of (b) to those of the results of the precious metals. Choose the correct answer below.

A. All three stock indices had lower returns than any of the precious metals. B. Silver had a much higher return than any of the three stock indices. Both gold and platinum had

a worse return than stock index C, but a better return than indices A and B.

C. Silver had a worse return than stock index C, but a better return than indices A and B. Gold had a better return than index B, but a worse return than indices A and C. Platinum had a worse return than all three stock indices.

D. All three stock indices had higher returns than any of the precious metals.

Year A B C 2012 8.61 12.77 15.85 2011 4.57 0.00 − 2.25 2010 11.00 11.54 16.18 2009 18.99 23.35 43.15

Metal Geometric mean rate of return Platinum %14.85

Gold %16.54 Silver %20.96

9.

4: Data table for total rate of return

5: Geometric mean rate of return for stock market indices

In 2009 2012, the value of precious metals changed rapidly. The data in the accompanying table represents the total rate of return (in percentage) for platinum, gold, and silver from 2009

–

through 2012. Complete parts (a) through (c) below.

Click the icon to view data table for total rate of return for platinum, gold, and silver.4 Click the icon to view the geometric mean rate of return for stock market indices.5

a. Compute the geometric mean rate of return per year for platinum, gold, and silver from 2009 through 2012.

The geometric mean rate of return for platinum during this time period was %. (Type an integer or decimal rounded to two decimal places as needed.)

The geometric mean rate of return for gold during this time period was %. (Type an integer or decimal rounded to two decimal places as needed.)

The geometric mean rate of return for silver during this time period was %. (Type an integer or decimal rounded to two decimal places as needed.)

b. What conclusions can you reach concerning the geometric mean rates of return of the three precious metals?

A. Platinum had a higher return than silver and a much higher return than gold. B. Platinum had a much higher return than silver and gold. C. Silver had a much higher return than gold and platinum. D. Gold had a higher return than silver and a much higher return than platinum.

c. Compare the results of (b) to those of the results of the stock indices. Choose the correct answer below.

A. Silver had a much higher return than any of the three stock indices. Both gold and platinum had a worse return than stock index C, but a better return than indices A and B.

B. All three metals had lower returns than any of the stock indices. C. Silver had a worse return than stock index C, but a better return than indices A and B. Gold had

a better return than index B, but a worse return than indices A and C. Platinum had a worse return than all three stock indices.

D. All three metals had higher returns than any of the stock indices.

Year Platinum Gold Silver 2012 5.8 0.2 56.6 2011 − 23.9 9.6 − 9.1 2010 23.3 30.6 14.8 2009 55.1 23.5 46.3

Stock indices Geometric mean rate of return A %9.96 B %11.28 C %22.49

10.

11.

12.

13.

The half-life of a certain element is days, meaning every days the amount is cut in half. Complete parts (a) through (d) below.

15.5 15.5

(a) Fill in the following table.

Days Grams 0 40 15.5

31.0

46.5

(Round to two decimal places as needed.)

(b) What is the average percent change per day over the first days?15.5

% (Round to two decimal places as needed.)

(c) Write down an equation for the amount of the element left after d days in the form: A = A • (1 + r)0 d

A = 40 • (1 − 4.37%)d

A = 40 • (1 + 4.37%)d

A = 40 • (0.0437)d

A = 40 • (1.0437)d

(d) How much is left after 3 days?

grams (Round to one decimal place as needed.)

The average cost of gas dropped from a high of $ per gallon on June 1, 2015 to a low of $ on February 1, 2016. Complete parts (a) through (c) below.

2.81 1.65

(a) What is the average percent change in gas price per month?

% (Round to one decimal place as needed.)

(b) What is the decay factor associated to this rate?

(Round to three decimal places as needed.)

(c) Write down an equation for the price of gas m months after June 1, 2015 in the form: P = P • (1 + r)0 m

A. P = 2.81 • (1 − 0.936)m

B. P = 2.81 • (1.064)m

C. P = 2.81 • (0.064)m

D. P = 2.81 • (0.936)m

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