A town has a population of 4000 and grows at 2% every year. To the nearest year, how long will it be until the population will reach 5100?

Answer 1

The exponential growth law for this problem is

P(t) = 4000 (1.02)^t

where t is years elapsed since the population was 4000. Set P(t)=5100 and solve for t.

5100 = 4000 (1.02)^t

5100 / 4000 = 1.02^t

log(5100 / 4000) = t log1.02

You can finish from here. Use any base for the log as long as it is the same in both places.

Answer 2

5100 = 4000 * (1.02)^ t

5100/4000 = 1.02^t

1.25 = 1.02^t

log 1.25 = t * log 1.02

t = log 1.25 / log 1.02

= 11.26