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

The function is

• y=400(1.22)^t

As per y=ab^x

• 1.22 is the rate of change

Its growth as it's greater than 1

The percentage increase is

• 1.22-1
• 0.22
• 22%

Answer 2

• Growth
• 22%

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.