Given:
The number of alligators in a wildlife is given by the function
[tex]f(x)=3450(1.04)^{x+1}[/tex]
To find:
The average growth rate of change from the 4th year to the 7th year.
Solution:
We have,
[tex]f(x)=3450(1.04)^{x+1}[/tex]
For x=4, we get
[tex]f(4)=3450(1.04)^{4+1}[/tex]
[tex]f(4)=3450(1.04)^{5}[/tex]
[tex]f(4)=4197.4525[/tex]
For x=7, we get
[tex]f(7)=3450(1.04)^{7+1}[/tex]
[tex]f(7)=3450(1.04)^{8}[/tex]
[tex]f(7)=4721.5632[/tex]
Now, the average growth rate of change from the 4th year to the 7th year is
[tex]m=\dfrac{f(7)-f(4)}{7-4}[/tex]
[tex]m=\dfrac{4721.5632-4197.4525}{3}[/tex]
[tex]m=\dfrac{524.1107}{3}[/tex]
[tex]m\approx 174.70[/tex]
Therefore, the average growth rate of the change from the 4th year to the 7th year is 174.70 per year.
