Question

the population of a town is represented by the formula p(t)=A(1.2)^t where A is the current population and t is time. determine to the nearest tenth of a year how long would it take the population to reach 5000 people if the current population is 3750

Answer 1

It would take 1.6 years.

The equation using our information would be:

`5000=3750(1.2)^t`

We would first divide both sides by 3750:

`(5000)/(3750)=(3750(1.2)^t)/(3750) \\ \\ (4)/(3)=1.2^t`

To solve for the exponent, we use logarithms:

`\log_(1.2)((4)/(3))=t \\ \\1.57788=t \\1.6 \approx t`