Question

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?

Answer 1

Answer:

• Growth
• 22%

Step-by-step explanation:

Given function:

• $P(t) = 400(1.22)^{t}$

Initial population size is when t = 0

• P(0) = 400(1.22)⁰ = 400(1) = 400

The multiple of 1.22 is applied every year, so the ratio of change is:

• 1.22 = 122% = 100% + 22%

This is an exponential growth which represents 22% annual growth.