Free Printable IM2: Exponential Growth and Decay 2022 F.LE

1.

In an exponential function, what does the ' $a$ ' represent?

a)

SLOPE

b)

RATE OF CHANGE

c)

Y-INTERCEPT

d)

COMMON RATIO

e)

Growth Factor

2.

What is $a$ , the starting term, for the function: $f\left(x\right)=300\left(1.16\right)^x$ ?

a)

$300$

b)

$1.16$

c)

$0.16$

d)

$x$

e)

$16$

3.

What is $b$ , the common ratio, for the function: $f\left(x\right)=300\left(1.16\right)^x$ ?

a)

$300$

b)

$1.16$

c)

$0.16$

d)

$x$

e)

$16$

4.

A population of 2200 beetles is too large to sustain and decreases in population each month at a rate of 5%. How would you write your decay factor, $b$ ?

a)

$-5$

b)

$-0.05$

c)

$0.95$

d)

$0.05$

e)

$5$

5.

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

a)

$0.08$

b)

$1.08$

c)

$0.92$

d)

$8$

e)

$-0.08$

6.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

$y=15\left(35\right)^x$

b)

$y=15\left(1.35\right)^x$

c)

$y=15\left(.35\right)^x$

d)

$y=35\left(1.15\right)^x$

e)

$y=0.35x+15$

7.

Classify the model as Exponential GROWTH or DECAY. $y=1200\left(0.85\right)^6$

a)

Growth

b)

Decay

8.

Classify the model as Exponential GROWTH or DECAY. $y=10\left(1.01\right)^3$

a)

Growth

b)

Decay

9.

Is the pictured graph growth, decay, or linear or none?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None

e)

Absolute Value

10.

Is this exponential growth or decay?

a)

Growth

b)

Decay

11.

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

12.

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

a)

y=5000(0.7)^x

b)

y=30(5000)^x

c)

y=5000(1.3)^x

d)

y=5000x^x

13.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

a)

14327

b)

4309

c)

839

d)

7680

14.

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

a)

$176,783.29

b)

$424,527.63

c)

$57,357.75

d)

$532,041,076.80

e)

$160,000

15.

Identify each function as representing exponential growth or decay. $f\left(x\right)=8932\left(0.68\right)^x$

a)

growth

b)

decay

16.

Is the following function growth or decay: $y=5\left(2\right)^x$

a)

Growth

b)

Decay

17.

Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. If no other money is added or withdrawn from the account, how much will be in the account after 10 years?

a)

$3122.18

b)

$4994.50

c)

$4440.73

d)

$86,776.40

e)

$3000.00

18.

After a dose of an antibiotic, the number of bacteria decreases. If the equation y = 15,000(0.63)^x models this “decay” situation, which value in the equation represents the original number of bacteria?

a)

0.63

b)

63

c)

15,000

d)

37

e)

0.37

19.

The number of kilograms, $y$ , of a radioactive element that remains after $x$ hours can be modeled by the equation

$y=0.32\left(.071\right)^x$

What is the rate of decrease of this radioactive element?

a)

$32\%$

b)

$71\%$

c)

$68\%$

d)

$29\%$

e)

$-71\%$

20.

The equation y = 512(1.09)^x models the value of an investment after x years. Which statement is true about the value of the investment?

a)

The value of the investment is increasing by $512 each year.

b)

The value of the investment is decreasing by $512 each year.

c)

The value of the investment is growing by 9% each year.

d)

The value of the investment is decaying by 9% each year.

21.

Is the function y = 2000(.30)^xgrowth or decay?

a)

growth

b)

decay

22.

Given the function y = 2000(.30)^x, what is the decay rate?

a)

30%

b)

70%

c)

2000

d)

1.30

e)

-30%

23.

Suppose you deposit $3000 in a savings account that pays interest at an annual rate of 4%. What is the growth factor?

a)

$-0.96$

b)

$1.4$

c)

$1.04$

d)

$3000

e)

$0.96$

24.

Since January 1980, the population of the city of Brownville has grown according to the mathematical model y=720,500(1.022)^x, where x is the number of years since January 1980. What is the was the population of Brownville in 1980?

a)

102.2 people

b)

720,500 people

c)

1.022 people

d)

1022 people

25.

James' 70 in. giant peach doubles in size every week. Write an expression that would represent how big the peach is after 5 weeks.

a)

70(2)³⁵

b)

70(2)⁵

c)

2(70)⁵

d)

5(70)²

e)

$5\left(3x\right)$

26.

A 78 gram sample of Uranium loses half of its mass each year. What is the exponential equation?

a)

y=78(0.5)^x

b)

y=78(1.5)^x

c)

y=78(2)^x

27.

Uber charges an initial fee of $2 plus $0.75 per mile. What type of function is this?

a)

Linear

b)

Exponential

c)

Neither

28.

Is the equation linear or exponential?

a)

Linear

b)

Exponential

29.

Is the equation linear or exponential?

a)

Linear

b)

Exponential

30.

Is the Equation Linear or Exponential?

a)

Linear

b)

Exponential

31.

Find the common ratio:
16, 4, 1, 0.25

a)

$\frac{1}{4}$

b)

$16$

c)

$4$

d)

$-12$

e)

$-4$

32.

A(n) _________________ function will ADD the same number each time.

a)

Linear

b)

Quadratic

c)

Exponential

d)

All of the above

33.

A(n) _________________ function will MULTIPLY the same number each time.

a)

Linear

b)

Quadratic

c)

Exponential

d)

All of them

34.

Is the table linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

35.

Maggie is knitting blankets for the residents of a local nursing home. She already has 6 blankets completed. After one week, Kay has 8 blankets. After two weeks, Kay has 10 blankets. Write the equation that represents this situation.

a)

y = 6x + 2

b)

y = 2x + 6

c)

y = 6(2)^x

d)

y = 2(6)^x

36.

True OR False: All increasing exponential functions eventually exceed all increasing linear functions.

a)

True

b)

False

37.

A tennis tournament begins with 128 players. At the end of round one, there will be 64 players. There are 32 players at the end of round 2 and 16 players remaining after round 3. Write the equation that best models this situation.

a)

y = 128x + 0.5

b)

y = 0.5x + 128

c)

y = 128(0.5)^x

d)

y = 128(0.5)^x-1

38.

Suppose you are saving for a new skateboard. You currently have $10 that you put in an envelope to save. Each week you put $5 in that envelope. If this were to be written as a function, how would 10 and 5 be represented?

a)

10 would be the slope; 5 would be the y-intercept

b)

10 would be the y-intercept; 5 would be the slope

c)

15 would be the y-intercept

d)

15 would be the slope

39.

The iPhone X is valued at $1000 upon purchase. The value is expected to decrease by 14% each year. What type of function is this?

a)

Linear

b)

Exponential

c)

Neither

40.

The iPhone X is valued at $1000 upon purchase. The value is expected to decrease by 14% each year. Which function matches the situation? Let Cost (C) be a function of time (t)

a)

C(t)=1000-0.14t

b)

C(t)=1000(.14)^t

c)

C(t)=1000(.86)^t

d)

C(t)=1000-0.86t

41.

The population of Cary, NC in the year 2000 was 97,400 people. The population steadily grew by 2.5% each year. Which function relates to the situation? Let Population (P) be a function of time (t)

a)

P(t)=97400+2.5t

b)

P(t)=97400(2.5)^t

c)

P(t)=97400(1.25)^t

d)

P(t)=97400(1.025)^t

42.

What type of function describes the story below?You have $5 and triple your money every day.

a)

Linear

b)

Quadratic

c)

Exponential

43.

Which function best models the amount of money you earn when you get paid an hourly wage?

a)

Linear

b)

Quadratic

c)

Exponential

44.

A bank account balance earning an annual interest rate.

a)

Linear

b)

Quadratic

c)

Exponential

45.

Is the graph linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

46.

Is the graph linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

47.

Is the graph linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

48.

Which function is linear?

a)

$f\left(x\right)$

b)

$h\left(x\right)$

c)

$g\left(x\right)$

IM2: Exponential Growth and Decay 2022 F.LE

Total questions: 48

Worksheet time: 1hrs 5mins

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