Question

Someone please help me ASAP

Answer 1

Given:

The number of alligators in a wildlife is given by the function

`f(x)=3450(1.04)^(x+1)`

To find:

The average growth rate of change from the 4th year to the 7th year.

Solution:

We have,

`f(x)=3450(1.04)^(x+1)`

For x=4, we get

`f(4)=3450(1.04)^(4+1)`

`f(4)=3450(1.04)^(5)`

`f(4)=4197.4525`

For x=7, we get

`f(7)=3450(1.04)^(7+1)`

`f(7)=3450(1.04)^(8)`

`f(7)=4721.5632`

Now, the average growth rate of change from the 4th year to the 7th year is

`m=(f(7)-f(4))/(7-4)`

`m=(4721.5632-4197.4525)/(3)`

`m=(524.1107)/(3)`

`m\approx 174.70`

Therefore, the average growth rate of the change from the 4th year to the 7th year is 174.70 per year.