A population of rabbits quadruples every 2 years If the init

A population of rabbits quadruples every 2 years. If the initial number of rabbits was 25, how long will it take for the population to reach 700??

I believe I understand how to solve the logarithm, I just don\'t understand how to extract the log it from the question.

Solution

The population of rabbits quadruples every 2 years. Let the number of years taken to reach 700 be T. The initial population is 25. This gives an equation:

700 = 25*(4)^(T/2)

=> 700/25 = 4^(T/2)

=> 28 = 4^(T/2)

take the log of both the sides

=> log 28 = (T/2)*log 4

=> T/2 = log 28/log 4

=> T = 2*(log 28/log 4)

=> T = 4.807 years.

The population of rabbits grows to 700 from 25 in 4.807 years.