Exponential Function

Question

A town has a population of 6000 and grows at 4% every year. To the nearest year, how long will it be until the population will reach 10100?

Answer 1

The equation for this problem is

p(t) = 6000 (1.04)^t

where t = years elapsed since when the population was 6000. Set p(t) equal to 10100 and solve for t.

10100 = 6000 (1.04)^t

10100/6000 = 1.04^t

log(10100/6000) = t log(1.04)

You should be able to finish from here. Use any base for the logs, as long as it is the same for both.