Exponential Functions — Test Answers

1

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What is the multiplicative rate of change of the function?

A

1 third

B

9

C

2

D

2 thirds

2

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What type of change does this represent?

A

an exponential change because the amount decreases by 10 percent of the current value each year

B

a linear change because the amount decreases by a fixed amount each year

C

an exponential change because the amount decreases by a fixed amount each year

D

a linear change because the amount decreases by 10 units each year

3

What is the multiplicative rate of change of the function?

A

3 fourths

B

3 halves

C

2 thirds

D

4 thirds

4

What value, written as a decimal, should Lena use as the common ratio?

A

2 point 0

B

1 point 5

C

1 point 0

D

2 point 5

5

How does the graph represent a situation where one quantity changes at a constant rate relative to another?

A

The distance increases as time increases.

B

The graph shows that time slows down as the car travels.

C

The graph flattens out as the car stops moving after 5 hours.

D

The upward slope shows the car is speeding up.

6

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 percent greater than the previous month’s total. She writes a recursive formula to describe the account balances. Which value should she use as the common ratio?

A

1 point 0 5

B

0 point 5

C

0 point 0 5

D

5 point 0

7

Which table represents exponential growth?

A

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1'; Column 2, '2' Row 3: Column 1, '2'; Column 2, '4' Row 4: Column 1, '3'; Column 2, '6' Row 5: Column 1, '4'; Column 2, '8'

B

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1'; Column 2, '2' Row 3: Column 1, '2'; Column 2, '4' Row 4: Column 1, '3'; Column 2, '7' Row 5: Column 1, '4'; Column 2, '11'

C

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1'; Column 2, '2' Row 3: Column 1, '2'; Column 2, '4' Row 4: Column 1, '3'; Column 2, '6' Row 5: Column 1, '4'; Column 2, '10'

D

Table with 2 columns and 5 rows.Row 1: Column 1, 'x'; Column 2, 'y' Row 2: Column 1, '1'; Column 2, '2' Row 3: Column 1, '2'; Column 2, '4' Row 4: Column 1, '3'; Column 2, '8' Row 5: Column 1, '4'; Column 2, '16'

8

The function f of x is equal to 2 times 5 to the x th power can be used to represent the curve through the points 1 comma 10 , 2 comma 50 , and 3 comma 250 What is the multiplicative rate of change of the function?

A

2

B

32

C

5

D

10

9

Which is the graph of f of x is equal to 1 fourth times 4 to the x th power ?

A

Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 with an increment of 1 and y axis is ranges from negative 6 to 6 with increment of 1. An exponential function approaches y equal to 0 in quadrant II and passes through points 1 comma 1 and 2 comma 4. The arrow is present on both ends of curve.

B

Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 with an increment of 1 and y axis is ranges from negative 6 to 6 with increment of 1. An exponential function approaches y equal to 0 in quadrant I. The curves up to the left and passes through points 0 comma 4 and 1 comma 1. The arrow is present on both ends of curve.

C

Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 with an increment of 1 and y axis is ranges from negative 6 to 6 with increment of 1. An exponential function approaches y equal to 0 in quadrant II and passes through points 3 comma 2 and 4 comma 4. The arrow is present on both ends of curve.

D

Image with description On a coordinate plane, the x axis ranges from negative 5 to 5 with an increment of 1 and y axis is ranges from negative 6 to 6 with increment of 1. An exponential function approaches y equal to 0 in quadrant I. The curves up to the left and passes through points 2 comma 1 and 0 comma 4. The arrow is present on both ends of curve.

10

Match each expression to the exponent rule that applies.

Answer:

Product of Powers|Quotient of Powers|Power of a Power

11

What is the simplified form of (5⁢e^2)⁢(−6⁢e^0)^2 ?

A

150 e squared

B

180 e squared

C

5 e squared

D

180 e

12

Which graph is the sequence defined by the function f of x is equal to 3 times 2 raised to the x minus 1 power ?

A

Image with description A coordinate plane with plotted points. The x-axis is labeled from 0 to 5 in increments of 1 and the y-axis is labeled from 0 to 180 in increments of 20. There are 5 points plotted on the plane showing an increasing exponential trend, a point at 1 comma 2, a point at 2 comma 6, a point at 3 comma 18, a point at 4 comma 54, and a point at 5 comma 162.

B

Image with description A coordinate plane with plotted points. The x-axis is labeled from 0 to 5 in increments of 1 and the y-axis is labeled from 0 to 180 in increments of 20. There are 5 points plotted on the plane showing an increasing exponential trend, a point at 0 comma 2, a point at 1 comma 6, a point at 2 comma 18, a point at 3 comma 54, and a point at 4 comma 162.

C

Image with description A coordinate plane with plotted points. The x-axis is labeled from 0 to 5 in increments of 1 and the y-axis is labeled from 0 to 180 in increments of 20. There are 5 points plotted on the plane showing an increasing exponential trend, a point at 1 comma 3, a point at 2 comma 6, a point at 3 comma 12, a point at 4 comma 24, and a point at 5 comma 48.

D

Image with description A coordinate plane with plotted points. The x-axis is labeled from 0 to 5 in increments of 1 and the y-axis is labeled from 0 to 180 in increments of 20. There are six points plotted on the plane showing an increasing exponential trend, a point at 0 comma 3, a point at 1 comma 6, a point at 2 comma 12, a point at 3 comma 24, a point at 4 comma 48, and a point at 5 comma 96.

13

Which is the graph of f of x is equal to 4 times 1 half to the x th power ?

A

Image with description A coordinate plane displays the x-axis labeled from negative 3 to 7 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1. A decreasing curve passes through approximately the points 0 comma 4, 1 comma 2, 2 comma 1, and 3 comma 0.5.

B

Image with description A coordinate plane displays the x-axis labeled from negative 3 to 7 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1. A decreasing curve passes through approximately the points 0 comma 4, 1 comma 2, 2 comma 1, and 4 comma 0.25.

C

Image with description A coordinate plane displays the x-axis labeled from negative 3 to 7 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1. A decreasing curve passes through approximately the points 0 comma 2, 1 comma 0.7, 2 comma 0.25, and 4 comma 0.05.

D

Image with description A coordinate plane displays the x-axis labeled from negative 3 to 7 in increments of 1 and the y-axis labeled from negative 3 to 7 in increments of 1. A decreasing curve passes through approximately the points 0 comma 2, 1 comma 1.3, 2 comma 1, and 6 comma 0.3.

14

Which formula can be used to describe the sequence? 1 point 2 comma 3 comma 7 point 5 comma 18 point 7 5 comma dot dot dot

A

f of x is equal to 2 point 5 times 1 point 2 raised to the x minus 1 power

B

f of x is equal to 1 point 2 times 2 point 5 to the x th power

C

f of x is equal to 2 point 5 times 1 point 2 to the x th power

D

f of x is equal to 1 point 2 times 2 point 5 raised to the x minus 1 power

15

Anabelle simplifies the expression (2⁢x)^3 (2⁢x)^3=2^3⋅x^3=8⁢x^3 Which property did Anabelle use to simplify the expression?

A

Product of Powers

B

Power of a Product

C

Power of a Power

D

Quotient of Powers

16

Read the scenario. A cell phone battery drains from 100 percent to 0 percent over 4 hours while playing videos continuously. Is one quantity changing at a constant rate relative to another in this scenario?

A

No, because other apps may be open on the phone.

B

No, because the battery drain can vary based on usage.

C

Yes, because the battery life decreases over time.

D

Yes, because the phone is being used continuously.

17

What is the simplified form of ((35⁢x^5⁢y^8)^0⁢(2⁢x⁢y^2)^−2)/(−3⁢(3⁢x^2)⁢(x⁢y^−2)) ?

A

the fraction with numerator 1 and denominator 36 x squared y squared

B

negative the fraction with numerator 1 and denominator 36 x to the negative 6 power y to the negative 8 power

C

negative the fraction with numerator 1 and denominator 36 x y to the 8th power

D

negative the fraction with numerator 1 and denominator 36 x to the 5th power y squared

18

What is the common ratio of the sequence? negative 2 comma 6 comma negative 18 comma 54 comma dot dot dot

A

8

B

negative 2

C

negative 3

D

3

19

The curve through the ordered pairs 0 comma 10 , 1 comma 5 , and 2 comma 2 point 5 can be represented by the function f of x is equal to 10 times 0 point 5 to the x th power What is the multiplicative rate of change of the function?

A

5

B

2 point 5

C

2

D

0 point 5

20

What does the formula A=1,500⁢(1.05)^t represent?

A

a principal of $1,500 decreasing by 5% per year

B

a principal of $1,500 increasing by 5% annually

C

a principal of $1,500 increasing by 50% annually

D

a loan of $1,500 with simple interest

Exponential Functions — Test Answers

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