The population of a certain town doubles in 14 years. How long will it take for the population to triple? Assume that the rate of increase of the population is proportional to the population.
A) 18.2 years
B) 20.2 years
C) 22.2 years
D) 23.2 years
E) 24.2 years

Question

Quizplus · Accepted Answer

Let P be the population of the town, measured in some units, and let t be the time, measured in years. Then, according to the problem, we have:

P(t) = P(0)*2^(t/14), where P(0) is the initial population.

We want to find the time T such that the population becomes three times its initial value, i.e.:

P(T) = 3*P(0)

Substituting the formula for P(t) into this equation, we get:

P(0)*2^(T/14) = 3*P(0)

Dividing both sides by P(0) and taking the logarithm with base 2, we obtain:

T/14 = log2(3)

T = 14*log2(3) ≈ 22.2

Therefore, the answer is C: 22.2 years.

The Population of a Certain Town Doubles in 14 Years