Free Printable Modeling with exponential functions

1.

The current population of Morristown is $19,000$ and is growing at 1.75% annually. Which function models this?

a)

$19,000\left(1.75\right)^t$

b)

$19,000\left(1+1.75\right)^t$

c)

$19,000\left(1+0.0175\right)^t$

d)

$19,000\left(1+0.000175\right)^t$

2.

In 1349, the Black Plague killed about one hundred million people. Every year after that, the number of fatalities due to the Black Plague decreased by $27\%$ . Which function models this?

a)

$100,000,000\left(28\right)^t$

b)

$100,000,000\left(1.27\right)^t$

c)

$100,000,000\left(0.73\right)^t$

d)

$100,000,000\left(0.66\right)^t$

3.

The temperature in a freezing car begins at 10o F. Every 10 minutes, the temperature increases by 40%. What's the temperature (in Fahrenheit) of the car 30 minutes after it has been started?

a)

$10\left(1.4\right)^3$

b)

$10\left(1.4\right)^{30}$

c)

$10\left(0.6\right)^3$

d)

$10\left(41\right)^{30}$

4.

Mr. Savage has $8,000,000 in his bank account, which accrues 1.932% interest every 3 months. How much money will be in his bank account after 9 years?

a)

$8,000,000\left(2.932\right)^{36}$

b)

$8,000,000\left(1.932\right)^9$

c)

$8,000,000\left(1.01932\right)^9$

d)

$8,000,000\left(1.01932\right)^{36}$

5.

You open a bank account with $1. The bank gives you four plans to choose from. Which plan will earn you the most money by the end of the year?

a)

Earn 100% interest 1 time per year

b)

Earn 50% interest 2 times per year

c)

Earn 25% interest 4 times per year

d)

Earn 5% interest 20 times per year

e)

All plans have the same effect

6.

There were 417 cell phones sold at an electronics store in January. Since then, cell phone sales at this store have increased at a rate of 3.75% per month. At this rate of growth, which function can be used to determine the monthly cell phone sales x months after January?

a)

f(x) = 417(3.75)^x

b)

f(x) = 417(0.0375)^x

c)

f(x) = 417(1.0375)^x

d)

f(x) = 417(1.375)^x

7.

A child asks her dad for an allowance that starts with a penny and then doubles every day for a month. Which function can be used to model the amount of money, A, the child will receive each day, x?

a)

A(x) = 2(0.01)^x

b)

A(x) = 0.01(2)^x

c)

A(x) = 0.01(1 - 2)^x

d)

A(x) = 2(1.01)^x

8.

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. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

9.

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

10.

A website allows its users to submit and edit content in an online encyclopedia. The graph shows the number of articles a(t) in the encyclopedia months after the website goes live.

How many articles were in the encyclopedia when it went live?

a)

0

b)

30

c)

60

d)

180

11.

In a carefully controlled biology lab, a population of 100 bacteria reproduces exponentially. Every hour, each bacteria splits into two bacteria.

Assuming no bacteria deaths, a function in the form

f(t) = ab^t can be used to model the growth of the bacteria population.

What would be the value of a?

a)

100

b)

0.5

c)

2

d)

50

12.

In a carefully controlled biology lab, a population of 100 bacteria reproduces exponentially. Every hour, each bacteria splits into two bacteria.

Assuming no bacteria deaths, a function in the form

f(t) = ab^t can be used to model the growth of the bacteria population.

What would be the value of b?

a)

100

b)

0.5

c)

50

d)

2

13.

Which of the following function describe exponential growth? Select all that apply.

a)

f(t) = 1.25^t

b)

f(t) = 2(0.93)^t

c)

f(t) = 3(1.07)^3t

d)

f(t) = 0.5(1.05)^t

e)

f(t) = 3(1.71)^5t

14.

The value of Amy's car depreciated each year after she bought it.

The function v(t) = 24,893(0.88)^t represents the value of Amy's car t years after she bought it.

What is the rate of depreciation?

a)

0.12%

b)

0.88%

c)

12%

d)

88%

15.

The Miller family and the Adams family both purchased houses on the same day several years ago.

The Miller family bought their house for $159,352 and it has been increasing in value by 3.7% each year.

The value of the Adams family’s home since it was purchased, A(x) , can be modeled by the function A(x) = 142,809(1.04)^x, where x represents the number of years since the house was purchased.

Which family's home value is increasing at a faster rate?

a)

The Miller family

b)

The Adams family

16.

This equation shows.....

a)

Exponential Decay

b)

Exponential Growth

c)

Linear Function

d)

None of these

17.

This equation shows.....

a)

Exponential Decay

b)

Exponential Growth

c)

Linear Function

d)

None of these

18.

Caiden earned $475 from mowing lawns last summer.He deposited this money in an account that pays an interest rate of 3.8% compounded annually. What will be his balance after 15 years?

a)

$827.52

b)

$831.10

c)

$839.45

d)

$846.80

19.

Emily’s parents put $1,500 in her bank account for college tuition. At an interest rate of 8.25% compounded semiannually,what will be the balance after 18 years?

a)

$6,273.50

b)

$6,314.08

c)

$6,385.72

d)

$6,427.94

20.

Mark took a loan out for $25,690 to purchase a truck. At an interest rate of 5.2% compounded monthly, how much total will he have paid after 5 years?

a)

$33,299.42

b)

$33,672.68

c)

$34,157.04

d)

$34,710.88

21.

Olivia would like to buy some new furniture for her home. She decides to buy the furniture on credit with 9.5% interest compounded quarterly. If she spent $7,400, how much total will she have paid after 8 years?

a)

$15,415.94

b)

$15,683.28

c)

$15,927.56

d)

$16,349.72

22.

Kennedy won $3,000 from a radio contest. If she puts this money in a bank account that earns 2.9% interest compounded quarterly, how much interest will she earn in 10 years?

a)

$915.59

b)

$933.28

c)

$979.81

d)

$1,005.09

23.

Town Bank offers a 2.25% interest rate, while Charter One offers 2.8%. Both banks compound interest annually. If Rob wants to set up a new account with $5,000,how much more money will he earn at Charter One over Town Bank after 25 years?

a)

$1,183.41

b)

$1,209.79

c)

$1,251.63

d)

$1,324.10

24.

What equation would yield a transformation right 3 units if your initial function was y=2^x

a)

y=2^x-3

b)

y=2^x+3

c)

y=2^x+³

d)

y=2^x-³

25.

Compare f(x) = 3^x- 4 with the basic function g(x) = 3^x

a)

4 units up

b)

4 units to the left

c)

4 units to the right

d)

4 units down

26.

What transformations have happened to f(x) = 2^x if the new equation is
g(x) = -2^(x+3) -6

a)

It stayed the same

b)

reflects, up 3, left 6

c)

reflects, right 3, down 6

d)

reflects, left 3, down 6

27.

A flea medicine breaks down at a rate of 20% per hour. This is the rate of decay of the medicine. The initial dose is 60 milligrams. Which of the following represent the equation the models the amount of flea medicine left in an animal?

a)

$y=60\left(.2\right)^x$

b)

$y=20\left(60\right)^x$

c)

$y=60\left(.8\right)^x$

d)

$y=60\left(1.2\right)^x$

28.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

29.

Select all the equations that represent exponential decay.

a)

$y=\frac{1}{2}\left(4\right)^x$

b)

$y=4\left(\frac{1}{2}\right)^x$

c)

$y=80\left(1.4\right)^x$

d)

$y=60\left(0.7\right)^x$

e)

$y=3\left(0.6\right)^x$

30.

This is an example of:

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

31.

This is an example of: $f\left(x\right)=\ 0.25\ \left(\ 1.3\right)^x$

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

32.

How do you know that this was exponential growth? $f\left(x\right)=0\ .25\ \left(\ 1.3\right)^x$

a)

Because the 0.25 was bigger than one

b)

Because the 1.3 was bigger than one

c)

Because the 0.25 was less than one

d)

Because the 1.3 was less than one

33.

This is an example of: $f\left(x\right)=90\ \left(\ \frac{1}{2}\right)^x$

a)

Linear Growth

b)

Linear Decay

c)

Exponential Growth

d)

Exponential Decay

34.

Is this exponential growth or decay?

a)

Growth

b)

Decay

Modeling with exponential functions

Total questions: 34

Worksheet time: 2hrs 39mins

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