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.
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.