Final answer:
To determine the future number of rabbits with an initial count of 80 and an addition of 10 baby rabbits per momma rabbit monthly, we use the function R(n) = 80 + 800n, where n is the number of months into the future. This linear model assumes only the initial rabbits are breeding and does not account for their offspring reproducing.
Step-by-step explanation:
To calculate the future rabbit population, given an initial count of 80 rabbits and the assumption that each momma rabbit has 10 babies every month, we need to create a function that models this growth. Our function will be linear because the number of new rabbits added each month is constant.
Let's define the variables:
- n = number of months in the future
- R(n) = total number of rabbits after n months
If we assume that only the initial 80 rabbits are reproducing, the function is:
R(n) = 80 + 800n
However, if every new female rabbit also starts producing babies, this becomes a much more complex problem involving exponential growth, which is not directly addressed by the information given. We'll use the simpler linear model for this exercise, which does not account for the offspring also reproducing.
Therefore, after n months, the total number of rabbits can be expected to be:
R(n) = 80 + 800n