A town has a population of 12000 and grows at 4% every year. To the nearest tenth of a year, how long will it be until the population will reach 18500?

11.0 years

Step-by-step explanation:

The exponential function describing the population growth can be written ...

population = (initial population) * (1 + growth rate) ^years

If t represents the number of years, we can fill in the values to get ...

18500 = 12000*1.04^t

Dividing by 12000 gives ...

18500/12000 = 1.04^t

Taking logarithms, we have ...

log (18500/12000) = t*log (1.04)

t = log (185/120) / log (1.04) ≈ 11.037 ≈ 11.0

It will be 11.0 years until the population reaches 18,500.