# EXPONENTIAL GROWTH OR DECAY FUNCTION FROM WORD PROBLEMS WORKSHEET

Write an exponential function to model each situation. Find each amount at the end of the specified time. Round your answers to the nearest whole number.

Problem 1 :

A town with a population of 5,000 grows 3% per year. Find the population at the end of 10 years.

Solution

Problem 2 :

Amy makes an initial investment of \$5000. The investment loses 13.5% each year. Find the amount Amy has at the end of 8 years.

Solution

Problem 3 :

Suppose you deposit \$1000 in a college fund that pays 7.2% interest compounded annually. Find the account balance after 5 years.

Solution

Problem 4 :

Suppose you deposit \$1000 in a college fund that pays 7.2% interest. Find the account balance after 5 years.

Suppose the account above paid interest quarterly instead of annually. Find the account balance after 5 years.

Solution

Problem 5 :

The population of Boomtown is 475,000 and is increasing at a rate of 3.75% each year. When will the population exceed 1 million people (to the nearest year)?

Solution

Problem 6 :

The population of Leavetown is 123,000 and is decreasing at a rate of 2.375% each year.

• When will the population of Leave town drop below 50,000 (to the nearest year)?
• What will the population of Leave town be 100 years from now?

Solution

Problem 7 :

The 1989 population of Mexico was estimated at 87,000,000. The annual growth rate is 2.4%. When will the population reach 100,000,000 (to the nearest year)?

Solution

Problem 8 :

The population of Small town in the year 1890 was 6,250. Since then, it has increased at a rate of 3.75% each year

a) What was the population of Small town in the year 1915?

b) In 1940?

c) What will the population of Small town be in the year 2003?

d) When will the population reach 1,000,000 (to the nearest year)?

Solution

Problem 9 :

A radioactive element decays at a rate of 5% annually. There are 40 grams of the substance present.

a) How much of the substance remains after 30 years

b) When will the amount of the substance drop to below 20 grams ?

Solution

1)  So, 6720 is the population after 10 years.

2)  So, at the end of 8 years the amount will be \$1567.

3)  So, after 5 years he will receive \$1416.

4)  So, after 5 years he will receive \$1429.

5)  After 22 years the population will be more than 1 million.

6)  After 37 years the population will drop below 50000.

11118

7)  So after 6 years, the population will be 100,000,000.

8) a) P = 15689,  b) P = 39381,  c) P = 400439,   d) x = 147

9)  a) P = 8.58

b) x = 14

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