Free Printable Unit 7 Test Study Guide

Worksheets

Unit 7 Test Study Guide

Total questions: 25

Worksheet time: 2hrs 34mins

Name

Class

Date

$f\left(x\right)=68\left(3\right)^x$

Consider the function for cell duplication. The cells duplicate every minute. What do the 68 and 3 represent in relation to the duplication of cells?

The 68 is the initial number of cells, and the 3 indicates that the number of cells increases by 3 every hour.

The 68 is the initial number of cells, and the 3 indicates that the number of cells triples every minute.

The 68 is the number of cells at 3 minutes and the 3 indicates that the number of cells increase by three every minute.

The 68 is the number of cells at one minute, and the 3 indicates that the number of cells decreases by three every 3 minutes.

Michael has a savings account. The total amount of money, in dollars, in the account in relation to the time, in years, since Michael made his first deposit can be described by the equation $A=450\left(1+.07\right)^t$ .

Initial Deposit (a)

Growth Factor (b)

Time (c)

Interest Rate (d)

Choose from the below words

70%

450

(1 + .07)

.07

A scientist is studying a population of bacteria. She uses the function $f\left(d\right)=654\left(0.23\right)^d$ to represent the number of bacteria each day, d. Which statement is the best interpretation of this function?

The initial bumber of bacteria decreases at a rate of 23% each day.

The initial number of bacteria increases at a rate of 77% each day.

The initial bumber of bacteria decreases at a rate of 77% each day.

The initial bumber of bacteria increases at a rate of 23% each day.

The function $4\left(3\right)^t$ models the amount of blooms on a chrysanthemum plant, where t represents the number of weeks since it was transplanted. Which statement is the best interpretation of one of the values in this function?

The number of blooms increases by 4 each week

The initial number of blooms on the plant was 3

The initial number of blooms on the plant was 4

The number of blooms on the plant increases by 3% each week

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. In how many months will there be 9,766 mosquitoes?

3 months

4 months

5 months

6 months

8^3x+3 = 8⁶

x=28

x=3

x=1

x=12

Solve the following exponential equation.

$9^{8-x}=27^{x-3}$

$x=5$

$x=-5$

$x=\frac{1}{5}$

$x=-\frac{1}{5}$

Solve for x.

3³ = 3^{4x + 2}

x = ¼

x = -¼

x = ½

x = -½

x = 0.24

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation?

y=8(15,000)^x

y=15,000(1.08)^x

y=15,000(0.92)^x

y=15,000(0.08)^x

10.

Given the following table of values, construct the function that represents the sequence.

y = 3(4)^x

y = 3x + 4

y = 4(3)^x

y = 4x + 3

11.

Which could be the graph of $f\left(x\right)=2\left(3\right)^x$

12.

A country is reducing it's government spending. The country's annual debt is modeled by $y=800\left(0.54\right)^t$ , where y is in billions of dollars and t represents the number of years since 2020. What is the percent decrease of the country's annual debt?

54%

46%

800%

0.54%

13.

A scientist is studying the amount of leaves on a plant. They notice that the plant starts with 3 leaves and the amount of leaves doubles each week. Which graph best models this situation if the scientist keeps studying the plant for x weeks.

14.

Evaluate
g(x) = 3(2)^x ; g(3) = ___

216

15.

A population of fish starts at 8,000 and decreases by 6% per year. Use an exponential function to find the population of fish in 10 years.

Round to the nearest whole number.

(a)

16.

Graph the function $g\left(x\right)=2\left(\frac{1}{3}\right)^x$ . Which features are correctly stated? PICK THREE

asypmtote: y = 0

y-intercept: (0, -1)

x-intercept: (0, 0)

y-intercept: (0, 2)

Contains the point (-1, 6)

17.

Caiden earned $475 from mowing lawns last summer. He deposited this money in an account that pays an interest rate of 3.8% compounded monthly. BY HOW MUCH will be his balance grow after 2 years?

$1162.60

$831.10

$37.45

$512.45

18.

Consider that $79\left(1.3\right)^x$ models the number of deer in the thousands in the state of Georgia at the end of x years since 2012. Which statement is the best interpretation of one of the values in this function?

The number of deer increases by 30 each year

The number of deer decreases by 30% each year

The number of deer in 2012 was 79,000

The first deer found in Georgia was 79 years ago

19.

Evaluate the exponential function

f(x) = 3^x ; x = - 2

-81

-9

1/9

-1/81

20.

What is the GROWTH FACTOR for the function: f(x) = 300(1.16)^x?

300

1.16

.16

21.

Rebecca has a savings account. The total amount of money, in dollars, in the account in relation to the time, in years, since Rebecca made her first deposit can be described by the equation $A=500\left(1+0.06\right)^t$ . Which of the following choices BEST describes Rebecca's function.

The initial deposit was 500

The interest rate earned is 6%

The decay factor is 0.94

t represents number of years

A represents the initial deposit

22.

The number of yearbooks sold at Bainbridge high school each year since 2020 can be shown by the following function: f(x) = 300(1.16)^x

How many yearbooks were sold initially in the year 2020?

300

1.16

348

23.

The half-life of strontium-90 is 25 years. How much strontium-90 will remain after 100 years if the initial amount is 4.0 g?

3.0g

0.25mg

0.3g

0.25g

24.

Emily’s parents put $1,500 in her bank account for college tuition. At an interest rate of 8.5% compounded monthly, what will be the balance after 18 years?

$1,703.21

$6,314.08

$6,890.00

$5,141.44

25.

What is the y-intercept of the function?

(0, 2)

(0, 3)

(3, 0)

(2, 0)

100 %

Unit 7 Test Study Guide

Total questions: 25

Worksheet time: 2hrs 34mins

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