Question

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?

Answer 1

Answer:

  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.