Question

The population of a town grew from 20,000 to 28,000. The continuous growth rate is 15%. The equation mc024-1.jpg represents the situation, where t is the number of years the population has been growing. About how many years has the population of the town been growing? Use a calculator and round your answer to the nearest whole number.
2 years
9 years
17 years
22 years

Answer 1

Use 28,000 = 20,000 e^{0.15t}.
1.4 = e^{0.15t} ⇒ ln(1.4) = 0.15t ⇒ t = ln(1.4)/0.15 ≈ 2.24 years.

Rounded to the nearest whole number: 2 years.