Unit Test Answers

1

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What is the solution to the equation

A

mc012-2.jpg

B

mc012-3.jpg

C

mc012-4.jpg

D

mc012-5.jpg

1

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What is the common ratio of the sequence?-2, 6, -18, 54,...

A

−3

B

−2

C

3

D

8

2

Which equation describes the relationship between the variables in the table below?xy-11928146,561559,049

A

; each y-value is the previous y-value multiplied by 9.

B

; each y-value is the previous y-value plus 9 more than was added previously.

C

; each y-value is the previous y-value plus 9.

D

; each y-value is the previous y-value multiplied by another 9.

2

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equation represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number.

A

1 year

B

2 years

C

5 years

D

8 years

3

Which of the following describes the growth rate of the exponential function in the graph below?

A

For each x increase of 1, the y increases by a common difference of 3.

B

For each x increase of 1, the y increases by a common factor of 3.

C

For each x increase of 1, the y increases by 4 more than the previous increase.

D

For each x increase of 1, the y increases by doubling and then adding 1.

3

Yui makes a list of the balances in her savings account at the end of each month. She notices that each month’s total is 5% greater than the previous month’s total. She writes a recursive formula to describe the account balances.

A

0.05

B

0.5

C

1.05

D

5.0

4

Devon purchased a new car valued at $16,000 that depreciated continuously at a rate of 35%. Its current value is $2,000. The equation represents the situation, where t is the age of the car in years and r is the rate of depreciation. About how old is Devon’s car? Use a calculator and round your answer to the nearest whole number.

A

1 year

B

2 years

C

5 years

D

8 years

4

Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. After c years, Calvin has $658.80. Makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. After m years, Makayla has $613.04. What is the approximate difference in the number of years that Calvin and Makayla have their money invested?

A

Makayla invests her money 1 year longer.

B

Makayla invests her money 2 years longer.

C

Calvin invests his money 1 year longer.

D

Calvin invests his money 2 years longer.

5

An equation for the depreciation of a car is given by y = A(1 – r)t , where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?

A

3.3 years

B

5.0 years

C

5.6 years

D

6.6 years

6

Which equation describes the relationship between the variables in the table below?xy-11928146,561559,049

A

; each y-value is the previous y-value multiplied by 9.

B

; each y-value is the previous y-value plus 9 more than was added previously.

C

; each y-value is the previous y-value plus 9.

D

; each y-value is the previous y-value multiplied by another 9.

7

What is the sum of the first seven terms of the geometric series?3 + 12 + 48 + 192 + ...

A

4,372

B

12,288

C

16,383

D

65,535

8

Tables of values for two different functions are given below. Which statement is true?

A

The right function grows approximately 21 times faster than the left function over the interval 4 < x < 5.

B

The right function grows approximately 21 times slower than the left function over the interval 4 < x < 5.

C

The right function grows approximately 6 times faster than the left function over the interval 2 < x < 3.

D

The right function grows approximately 2.5 times slower than the left function over the interval 2 < x < 3.

9

The height of a plant over time is shown in the table below. Using a logarithmic model, what is the best estimate for the age of the plant when it is 19 inches tall?Plant Heightt, time in monthsh, height in inches118218.21318.33418.42518.48618.54

A

10 months

B

14 months

C

16 months

D

28 months

9

What is the true solution to the equation below?

A

and

B

and

C

and

D

and

10

A population of insects increases at a rate of 1.5% per day. About how long will it take the population to double?

A

2.5 days

B

5.0 days

C

46.6 days

D

66.7 days

10

Which geometric series converges?

A

StartFraction 1 Over 81 EndFraction + StartFraction 1 Over 27 EndFraction + one-ninth + one-third + ellipsis

B

1 + one-half + one-fourth + one-eighth + ellipsis

C

Sigma-Summation Underscript n = 1 Overscript infinity EndScripts 7 (negative 4) Superscript n minus 1

D

Sigma-Summation Underscript n = 1 Overscript infinity EndScripts one-fifth (2) Superscript n minus 1

10

What is the solution to the equation below?

A

mc008-2.jpg

B

mc008-3.jpg

C

mc008-4.jpg

D

mc008-5.jpg

11

A hospital sends an invoice to a patient. The patient schedules a payment plan in which she makes an initial payment of $1,451 the first month and then pays one-third of the previous month’s payment each of the following months until the invoice is paid in full. Approximately how much of the invoice will be paid after the fourth month?

A

$1,451.00

B

$2,095.89

C

$2,149.63

D

$2,167.54

12

What is the true solution to the equation below?

A

and

B

and

C

and

D

and

12

Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. After c years, Calvin has $658.80. Makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. After m years, Makayla has $613.04. What is the approximate difference in the number of years that Calvin and Makayla have their money invested?

A

Makayla invests her money 1 year longer.

B

Makayla invests her money 2 years longer.

C

Calvin invests his money 1 year longer.

D

Calvin invests his money 2 years longer.

12

What is the solution to the equation below?

A

mc008-2.jpg

B

mc008-3.jpg

C

mc008-4.jpg

D

mc008-5.jpg

13

The height of a plant over time is shown in the table below. Using a logarithmic model, what is the best estimate for the age of the plant when it is 19 inches tall?Plant Heightt, time in monthsh, height in inches118218.21318.33418.42518.48618.54

A

10 months

B

14 months

C

16 months

D

28 months

14

A painter is painting a wall with an area of 150 ft2. He decides to paint half of the wall and then take a break. After his break, he paints half of the remaining unpainted portion and then takes another break. If he continues to paint half of the remaining unpainted portion between breaks, approximately what portion of the original wall will be painted when he takes his fifth break?

A

112.50 ft2

B

145.31 ft2

C

147.66 ft2

D

290.63 ft2

15

Ajay analyzed two companies and has formulated tables to model each company’s growth, where x represents the age of the companies in years and y represents growth in terms of number of employees. Company 1 Company 2 If the number of employees is an indicator of a successful business, in which company should Ajay invest?

A

company 1 because it is adding six employees each year while company 2 is multiplying its number of employees by six each year

B

company 1 because it is multiplying its number of employees by six each year while company 2 is adding six employees each year

C

company 2 because it is adding six employees each year while company 1 is multiplying its number of employees by six each year

D

company 2 because it is multiplying its number of employees by six each year while company 1 is adding six employees each year

15

Ajay analyzed two companies and has formulated tables to model each company’s growth, where x represents the age of the companies in years and y represents growth in terms of number of employees. Company 1 Company 2 If the number of employees is an indicator of a successful business, in which company should Ajay invest?

A

company 1 because it is adding six employees each year while company 2 is multiplying its number of employees by six each year

B

company 1 because it is multiplying its number of employees by six each year while company 2 is adding six employees each year

C

company 2 because it is adding six employees each year while company 1 is multiplying its number of employees by six each year

D

company 2 because it is multiplying its number of employees by six each year while company 1 is adding six employees each year

16

Tables of values for two different functions are given below. Which statement is true?

A

The right function grows approximately 21 times faster than the left function over the interval 4 < x < 5.

B

The right function grows approximately 21 times slower than the left function over the interval 4 < x < 5.

C

The right function grows approximately 6 times faster than the left function over the interval 2 < x < 3.

D

The right function grows approximately 2.5 times slower than the left function over the interval 2 < x < 3.

16

1.2, 3, 7.5, 18.75, ...

A

f(x) = 1.2(2.5)x – 1

B

f(x) = 2.5(1.2)x – 1

C

f(x) = 1.2(2.5)x

D

f(x) = 2.5(1.2)x

17

An equation for the depreciation of a car is given by y = A(1 – r)t , where y = current value of the car, A = original cost, r = rate of depreciation, and t = time, in years. The value of a car is half what it originally cost. The rate of depreciation is 10%. Approximately how old is the car?

A

3.3 years

B

5.0 years

C

5.6 years

D

6.6 years

17

The equation for the pH of a substance is pH = –log[H+], where H+ is the concentration of hydrogen ions. A basic solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentration of hydrogen ions between the two solutions?

A

mc018-1.jpg

B

mc018-2.jpg

C

mc018-3.jpg

D

mc018-4.jpg

17

A population of insects increases at a rate of 1.5% per day. About how long will it take the population to double?

A

2.5 days

B

5.0 days

C

46.6 days

D

66.7 days

18

Which graph is the sequence defined by the function f(x) = 3(2)x-1?

A

On a coordinate plane, 5 points are plotted. The points are (0, 2), (1, 6), (2, 18), (3, 54), (4, 162).

B

On a coordinate plane, 5 points are plotted. The points are (1, 2), (2, 6), (3, 18), (4, 54), (5, 162).

C

On a coordinate plane, 6 points are plotted. The points are (0, 3), (1, 6), (2, 12), (3, 24), (4, 48), (5, 96).

D

On a coordinate plane, 5 points are plotted. The points are (1, 3), (2, 6), (3, 12), (4, 24), (5, 48).

18

Which is the graph of the sequence defined by the function f(x + 1) = f(x) if the initial value of the sequence is 108?

A

Option

B

Option

C

Option

D

Option

19

What is the value of r of the geometric series?

A

0.8

B

1.3

C

3.0

D

3.2

19

What is the solution to the equation

A

mc012-2.jpg

B

mc012-3.jpg

C

mc012-4.jpg

D

mc012-5.jpg

20

The estimated number of organisms in a population after t days is shown in the table below.t daysestimated number of organisms, n286041,25061,80082,600103,720Which equation best models the situation?

A

mc003-1.jpg

B

mc003-2.jpg

C

mc003-3.jpg

D

mc003-4.jpg

20

Which of the following describes the growth rate of the exponential function in the graph below?

A

For each x increase of 1, the y increases by a common difference of 3.

B

For each x increase of 1, the y increases by a common factor of 3.

C

For each x increase of 1, the y increases by 4 more than the previous increase.

D

For each x increase of 1, the y increases by doubling and then adding 1.

21

For which pair of functions is the exponential consistently growing at a faster rate than the quadratic over the interval ?

A

mc015-2.jpg

B

mc015-3.jpg

C

mc015-4.jpg

D

mc015-5.jpg

21

The atmospheric pressure at sea level is 14.7 lb/in2. This pressure is reduced by half for each 3.6 miles above sea level. Which graph correctly identifies the amount of atmospheric pressure based on height, in miles, above sea level?

A

mc027-1.jpg

B

mc027-2.jpg

C

mc027-3.jpg

D

mc027-4.jpg

21

What is the value of r of the geometric series?

A

0.8

B

1.3

C

3.0

D

3.2

22

What is the sum of the infinite geometric series?

A

–288

B

–216

C

–144

D

–72

22

A conservationist determines that a particular beach is eroding at a rate of 1.1% each year. When writing an explicit formula to represent the amount of beach remaining each year, which value should she use as the common ratio?

A

0.011

B

0.089

C

0.989

D

1.011

23

Lena is asked to write an explicit formula for the graphed geometric sequence.

A

1.0

B

1.5

C

2.5

D

2.0

23

A scientist has discovered an organism that produces five offspring exactly one hour after its own birth, and then goes on to live for one week without producing any additional offspring. Each replicated organism also replicates at the same rate. At hour one, there is one organism. At hour two, there are five more organisms. How many total organisms are there at hour seven?

A

2,801

B

19,531

C

19,607

D

97,655

24

What is the solution to the equation below?

A

mc010-2.jpg

B

mc010-3.jpg

C

mc010-4.jpg

D

mc010-5.jpg

24

The graph below shows the exponential function and the linear function .What is the minimum y-value after which the exponential function will always be greater than the linear function?