Question

A town has a population of 20000 and grows at 3.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 35300?

Answer 1

16.5 years

Explanation:

The exponential growth model usually applied to interest is also useful in this type of problem. Here,

initial population: 20,000

final population: 35,300

Annual interest rate: 3.5% <=> 0.035

Then A = P(1 + r)^t becomes

ln A = ln P + t*ln 1.035, so that

ln A - ln P 0.5682

t = ------------------ = -------------- = 16.5 years

ln 1.035 0.0344