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

$m=\dfrac{f(7)-f(4)}{7-4}$

$m=\dfrac{4721.5632-4197.4525}{3}$

$m=\dfrac{524.1107}{3}$

$m\approx 174.70$

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