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

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

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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.

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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.)

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