Question

A population of field mice is 120. The population increas es at a rate of 9% a year. Write an exponential function that models

this situation:

Answer 1

Population(year x) = 120*(1.09)^x

Explanation:

Let x be the number of years from the time the population is 120 (year 0).

Population(year x) = 120*(1.09)^x

The 1.09 represents the growth for 1 year added to the initial population. E.g., year 1 would have a population of 120*(1.09)^1 or 140.8 (141). Year 2 would be 120*(1.09)^2 or 142.5 (143). And so on.

Each new year bilds on the prior year's ending population. In longhamd, this would be:

Year Pop.

0 120 120*(1.09)^0

1 141 120*(1.09)

2 120*(1.09)(1.09) or 120*(1.09)^2

3 120*(1.09)(1.09)(1.09) or 120*(1.09)^3

and so on.