Question

The number of rabbits in a forest at time t, in months, is R(t)= 500[10+e^-t/10]
a. What is the initial number of rabbits in the forest?
b. Determine the rate of change of the number of rabbits at time t.
c. How fast is the number of rabbits changing after one year?
d. Determine the largest number of rabbits in the forest during the first three years.

Answer 1

@Astrophysics

Answer 2

@Miracrown

Answer 3

\[\large\rm R(\color{orangered}{t})=500\left(10+e^{-\color{orangered}{t}/10}\right)\]

For part a, the initial rabbit amount corresponds to time t=0,\[\large\rm R(\color{orangered}{0})=500\left(10+e^{-\color{orangered}{0}/10}\right)\]\[\large\rm R(\color{orangered}{0})=?\]