6. Let P(t) be the population of rabbits in an area, with t measured in months. Suppose that 2 months after t = 0 there are 2000 rabbits in the field and 3 months (after t = 0) there are 5000 rabbits. How many rabbits were there originally, i.e., at t = 0? Assume that the number of rabbits is growing exponentially.

Solution: We have P(t) = A e^kt where A and k are constants. In addition, we are given that

Now, solving for A

The second and last part of this string of equations give us our answer: