Question

The population of a small town is currently 6000. This population grows at roughly 1.6% per year. In how many years will the population of the town triple?

Answer 1

Answer: it will triple in 69.1 years.

Step-by-step explanation:

The growth rate is exponential. We would apply the formula for exponential growth which is expressed as

A = P(1 + r)^t

Where

A represents the population after t years.

t represents the number of years.

P represents the initial population.

r represents rate of growth.

From the information given,

P = 6000

A = 3 × 6000 = 18000

r = 1.6% = 1.6/100 = 0.016

Therefore

18000 = 6000(1 + 0.016)^t

18000/6000 = (1.016)^t

3 = (1.016)^t

Taking log of both sides to base 10

Log 3 = log1.016^t = tlog1.016

0.477 = 0.0069t

t = 0.477/0.0069

t = 69.1 years