A population of rabbits in a lab, r(x), can be modeled by the function r(x) = 30(1.02)^x, where x represents the number of days since the population was first counted. Determine, to the nearest tenth, the average rate of change from day 35 to 52, including units

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:

And we want to find the average rate of change from x = 35 to x = 52.

We can use the slope formula:

Our first point will be (35, r(35)) and our second point is (52, r(52)). Substitute:

Note that our outputs y are rabbits and our inputs or x are days. Substitute:

Use a calculator:

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.