The average rate of change is 2.25 times as fast, the correct option is D.
Given
The function [tex]\rm f(x)=400(1.5)^x[/tex] models an insect population after x months.
The Average Rate of Change function is defined as the average rate at which one quantity is changing with respect to something else changing.
The average rate of change between Months 2 and 4 is;
[tex]\rm Average \ rate \ of \ change =\dfrac{400(1.5)^4-400(1.5)^2}{4-2}\\\\Average \ rate \ of \ change =\dfrac{2025-900}{2}\\\\Average \ rate \ of \ change=\dfrac{1125}{2}\\\\Average \ rate \ of \ change=562.5[/tex]
The average rate of change between Months 0 and 2 is;
[tex]\rm Average \ rate \ of \ change =\dfrac{400(1.5)^2-400(1.5)^0}{2-0}\\\\Average \ rate \ of \ change =\dfrac{900-400}{2}\\\\Average \ rate \ of \ change=\dfrac{500}{2}\\\\Average \ rate \ of \ change=250[/tex]
Therefore,
The average rate of change between Months 2 and 4 compare to the average rate of change between Months 0 and 2 is;
[tex]\rm =\dfrac{Average \ rate \ of \ change \ 2 \ and \ 4}{Average \ rate \ of \ change \ 0 \ and \ 2}\\\\= \dfrac{562.5}{250}\\\\=2.25[/tex]
Hence, the average rate of change is 2.25 times as fast.
To know more about the average rate click the link given below.
https://brainly.com/question/20114400
