13 October, 03:48
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?
13 October, 05:16
Answer: it will triple in 69.1 years.
The growth rate is exponential. We would apply the formula for exponential growth which is expressed as
A = P (1 + r) ^t
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
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
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» 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?