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Exponential Equations Review

Total questions: 15

Worksheet time: 12mins

Name
Class
Date
1.

Ash has $8,000 in a savings account. The interest rate is 3% compounded once a year.

To the nearest cent, how much will he have in his account in 4 years?

a)

$9,004.07

b)

$2,2848.80

c)

$9,011.94

d)

$8,242.71

2.

A sailboat that costs $5,950 decreases in value by 11% per year. How much will the boat be worth after 6 years?

a)

$5,884.00

b)

$5,178.97

c)

$2,992.96

d)

$2,957.04

3.

The value of a car purchased for $20,000 decreases at a rate of 12% per year. What will be the value of the car after 3 years?

a)

$12,800.00

b)

$13,629.44

c)

$17,600.00

d)

$28,098.56

4.

Find the balance in an account that has $300 invested at 6.5% for 4 years compounded semi-annually.

a)

$387.47

b)

$496.50

c)

$7,800.00

d)

$385.94

5.

A city doubles its size every 64 years. If the population is currently 225,000, what will the population be in 128 years?

a)

The population will be 225,000.

b)

The population will be 450,000.

c)

The population will be 900,000.

d)

The population will be 1,800,000.

6.

Every time Pinocchio lies his nose grows 20%. The growth of his nose can be modeled by n(t)=2(1+.2)tn\left(t\right)=2\left(1+.2\right)^t  . What was the length of his nose originally?

a)

2

b)

2.4

c)

4.98

d)

7.17

7.

Scrooge invests in a bank account that pays him 4% interest annually. This can be modeled by p(t)=500(1.04)tp\left(t\right)=500\left(1.04\right)^t  . How much money did he place in the bank at the beginning of the account?

a)

4

b)

500

c)

608

d)

541

8.

Rapunzel's hair grew 16% each week she was in the tower. If her hair was 20 inches long when she was placed in the tower, what is a model for the growth of Rapunzel's hair?

a)

16(1+.20)w16\left(1+.20\right)^w  

b)

16(1+20)w16\left(1+20\right)^w  

c)

20(1+.16)w20\left(1+.16\right)^w  

d)

20(1+16)w20\left(1+16\right)^w  

9.

Which is the same as 300(1.17)t300\left(1-.17\right)^t  

a)

300(1.17)t300\left(1.17\right)^t  

b)

300(.83)t300\left(.83\right)^t  

c)

300(.93)t300\left(.93\right)^t  

10.

Is this exponential growth or decay? What is the rate?

y = 7(1.2)x

a)

Growth. Rate is 2%

b)

Decay. Rate is 20%

c)

Growth. Rate is 20%

d)

Decay. Rate is 2%

11.

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(0.35)x

c)

y = 15(1.35)x

d)

y = 35(1.15)x

12.

Does the following equation show growth or decay?

y=10,000(0.76)x

a)

Growth

b)

Decay

13.
You buy a new computer for $2100. The computer decreases by 50% annually. How much is it worth after 2 years.
a)
225
b)
325
c)
425
d)
525
14.
Bacteria can multiply at an alarming rate when each bacteria splits into two new cells, thus doubling. If we start with only one bacteria which can double every hour, how many bacteria will we have after half of a day?
a)
1024
b)
2048
c)
8192
d)
4096
15.
Each year the local country club sponsors a tennis tournament. Play starts with 256 participants. During each round, half of the players are eliminated. How many players remain after 5 rounds? 
a)
2
b)
4
c)
16
d)
8