# 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...

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.

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Expert Answers

justaguide | Certified Educator

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.**