Question

A statistician finds that the population P of a small developing country has been increasing at a rate of 3.65% annually. In 2000, the country's population was 2.1 million. If the country continues to grow at this rate, during which year will the population reach 3.6 million people? Use an exponential function to model the population and show your work.

Answer 1

15.035 years

Explanation:

The exponential function to calculate population growth is

P(t) = Poe^kt

P(t) = Population size after t years = 3.6 million

Po = Initial population size = 2.1 million

k = growth rate = 3.65% = 0.0365

t = time in years = ???

Hence:

3600000 = 2100000 × e ^0.0365t

Divide both sides by 2100000

3600000/2100000 = e^0.0365t

1.7142857143 = e^0.0365t

Find the log of both sides

Log 1.7142857143 = log (e^0.0365t)

Log 1.7142857143 /Log 0.0365 = t

t = 15.035 years