Answer:
The population of the rabbits in the lab grew, on average, at a rate of 1.4 rabbits per day from day 35 to 52.
Step-by-step explanation:
The average rate of change of a function between two points is essentially the slope between them.
We have the function:
[tex]r(x)=30(1.02)^x[/tex]
And we want to find the average rate of change from x = 35 to x = 52.
We can use the slope formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Our first point will be (35, r(35)) and our second point is (52, r(52)). Substitute:
[tex]\displaystyle m=\frac{r(52)-r(35)}{52-35}[/tex]
Note that our outputs y are rabbits and our inputs or x are days. Substitute:
[tex]\displaystyle m=\frac{30(1.02)^{52}-30(1.02)^{35} \text{ rabbits}}{52-35\text{ days}}[/tex]
Use a calculator:
[tex]\displaystyle m\approx\frac{1.4\text{ rabbits}}{\text{day}}[/tex]
So, the population of the rabbits in the lab grew on average at a rate of 1.4 rabbits per day from day 35 to 52.
