Answer the Questions of Exponential Growth and Decay

Question

A study is done on the population of a certain fish species in a lake. Suppose that the population size P(t) after t years is given by the following exponential function.

P(t) = 530(1.38) ^ t

1.

Find the initial population size.

2.

Does the function represent growth, or decay?

3.

By what percent does the population size change each year?

Answer 1

P(t) = 530(1.38) ^ t

1) Find the initial population size.

Initial population is when t = 0

P(0) = 530(1.38) ^ 0 = 530(1) = 530

Answer: 530 fish initially

2) Does the function represent growth, or decay?

Since the exponent t = 1.38 > 1, the population is growing.

3) By what percent does the population size change each year?

After 1 year, t = 1

P(1) = 530(1.38) ^ 1 = 530(1.38) = 731.4

Population change = (P(1) - P(0)) / P(0) = (731.4 - 530) / 530 = 0.38

Answer is 38%