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Exponential growth and decay

Total questions: 12

Worksheet time: 35mins

Name
Class
Date
1.
Which of the following functions shows an initial amount of $15 and an increase of 35% each year?
a)
y = 15(35)x
b)
y = 15(1.35)x
c)
y = 15(0.35)x
d)
y = 35(1.15)x
2.

The function to find the value of a car after t years is given by v(t) = 24,000(.75)t Which of the following statements is true?

a)

The starting value of the car was $24,000.

b)

The y-values of the graph increase as the x-values increase.

c)

The value of b indicates this is an exponential decay situation.

3.
Daniel’s Print Shop purchased a new printer for $35,000. Each year it depreciates at a rate of 5%. How much will the printer be worth in 8 years?
4 lines
4.

What is the initial value for the function: f(x) = 300(1.16)x?

4 lines
5.
The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.
a)
y=1400(1.09)x
b)
y=1.09(1400)x
c)
y=1400(.91)x
d)
y=1.09x
6.

Classify the model as Exponential growth or decay.

A=10(1.01)3

a)

Growth

b)

Decay

7.
Is the pictured graph growth, decay, or linear or none?  
a)
Growth
b)
Decay
c)
Linear
d)
None
8.

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

9.
a)
The graph represents an exponential growth situation.
b)
Eventually, the car will be worth exactly $0.
c)
The starting value of the car was $12,000.
d)
The range for the situation is y ≥ 0.
10.

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 If no other money is added or withdrawn from the account, how much will be in the account after 10 years?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

11.

What is a, the initial amount, for the function:

f(x)=300(1.16)x

a)

300

b)

1.16

c)

.16

d)

x

12.

Which graph is an exponential function?

a)

red

b)

blue

c)

green

d)

none