exponential growth

Question

The population of rabbits in a forest follows the law of exponential growth. If 90 rabbits are present initially and there are 180 after 3 years, how many will there be in 4 years?

Answer 1

Let N(t) = number of rabbits in t years

 

N(t) = 90e^kt

 

Since N(3) = 180, 90e^3k = 180

 

                               e^3k = 2

 

                                 3k = ln2     k = 0.231

 

N(t) = 90e^0.231t

 

So, N(4) = 90e^0.231(4) = 90e^0.924 ≈ 226 rabbits