A study is done on the population of a certain fish species in a lake. Suppose that the population size P(1) after years is given by the following exponential function.
P(t) = 400(1.22)
Find the initial population size.
Does the function represent growth or decay?
O growth O decay
By what percent does the population size change each year?

(1) A decay

(2) 22%

Step-by-step explanation:

(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.

(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%

(1st) A decay

(2nd) 22%

Step-by-step explanation:  

(1st)

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

(2nd)

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

=78/100×100=78%

(100-78) = 22%  

both equations and proportions are better.