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) = 420 (0.78) ^t

does the function represent growth or decay?

By what percentage does the population change each year?

Answer

part 1) A decay

part 2) 22%

Explanation

part 1

This is an exponential function.

The number been raised to the power of time is a fraction which is less than 1. This means that as the time increases the fraction is decreasing hence the population.

part 2

The formula for getting the population is P (t) = 420*〖0.78〗^t

This means that the current population is 420 and 0.78 is the percentage.

This will be equal to 0.78=78/100

As a percentage = 78/100*100=78%

This means that the population decrease by (100-78) = 22%