About how long will it take the population to reach 600 rabbits and 1200 rabbits?

Question

A population of 550 rabbits is increasing by 2.5% each year. The function y=5.5(1.025)^x gives the population of rabbits, in hundreds, x years from now.

Answer 1

Assuming the same growth rate = 2.5% per year

f(x) = Population

f(x) = 6 (1.025)^x 

12 = 6 (1.025)^x

2 = (1.025)^x

Log 2 = Log (1.025)^x

Log 2 = x Log (1.025)   Power Rule for Logarithms

x = Log 2 / Log (1.025) = 0.3010 / .0107 = 28.1  years

 

General rule is doubling time for exponential growth is 72 / %

So 72 / 2.5 = 28.8  checks about right