Question

A study of the annual population of deer in Georgia from 1972-2012, shows the population, D(t), can be represented by the function D(t) = 394,267(1.032)^t

Answer 1

`D(t)=394,267(1.003)^(12t)`

Explanation:

The complete question in the attached figure

we have

`D(t)=394,267(1.032)^t`

This is a exponential growth function

where

P(t) is the population

t is the number of years

The initial value is 394,267 people

The factor growth is 1.032

To find out the monthly rate of growth, rewrite the expression

Remember that one year is equal to 12 months

`D(t)=394,267(1.032)^{(t*(12)/(12))}`

`D(t)=394,267[(1.032)^{((1)/(12))}]^(12t)`

`D(t)=394,267(1.003)^(12t)`