Exponential Functions

Question

A town has a population of 2000 and grows at 4.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 3900?

Answer 1

Population after n years will be 2000(1.045)^n,

To determine after how many years will population reach 3900, solve:

2000(1.045)^n = 3900

(1.045)^n = 1.95

log 1.045^n = log 1.95

n log 1.045 = log 1.95

n = log 1.95/log 1.045 = 15.17 ~ 15.2 years.