Question

A study of black bears in the Adirondacks reveals that their population can be represented by the function , where is the number of years since the study began. Write a function that models the monthly growth rate (to the nearest hundredth of a percent) of the black bear population

Answer 1

`\mathbf{ P(t) = 3500 (1.}00206)^(12t)`

Explanation:

The missing value of the given function is:

`P(t) = 3500 (1.025)^t`

where

t = no. of years since study began

∴

`P(t) = 3500 (1+0.025)^t`

Per year, the function can be written as:

`P(t) = 3500 (1+(25)/(1000))^t`

For monthly growth rate m = 12

`P(t) = 3500 (1+(25)/(1000(m)))^(mt)`

`P(t) = 3500 (1+(25)/(1000(12)))^(12t)`

`P(t) = 3500 (1+(25)/(12000))^(12t)`

`P(t) = 3500 (1+0.00206)^(12t)`

`\mathbf{ P(t) = 3500 (1.}00206)^(12t)`