The initial population of a town is 3300​, and it grows with a doubling time of 3 years. Determine how long it will take for the population to quadruple.

Answer 1

This is an example of exponential growth. The growth law for this problem is

P(t) = 3300 (2)^t/3,

where t is the number of years elapsed. To find the time to quadruple, set

P(t) = 4(3300)

and solve for t.

4(3300) = 3300 (2)^t/3

4 = 2^t/3

log4 = (t/3) log2

You should be able to finish from here. Use any base for the logs as long as it is the same base for both logs.