Question

The population of a town is 15,000. It decreases at a rate of 8% per year. In about how many years

will the population be fewer than 10,000?

Answer 1

5

Explanation:

If a population is decreasing by 8% we can multiply the population by 92% (1-.08)

which means we have the following equation

population=15000(.92)ⁿ

where n is the number of years

we want to know when the population will be 10,000 so we write

10,000=15,000(.92)ⁿ

.66667=.92ⁿ

a rule we have is

`n=y^x\\log_yn=x`

which means that

`.66667=.92^n\\=log_(.92).66667`

compute this and get

4.867

round this up to 5