Question

The formula A=200e^.033t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 297 thousand?

Answer 1

In the year 2010

Explanation:

we have

`A=200e^(0.033t)`

where

A is the population in thousands

t is the number of years since 1998

so

For A=297 thousands

substitute and solve for t

`297=200e^(0.033t)`

simplify

`1.485=e^(0.033t)`

Apply ln both sides

`ln(1.485)=ln[e^(0.033t)]`

`ln(1.485)=(0.033t)ln(e)`

Remember that

`ln(e)=1`

`ln(1.485)=(0.033t)`

`t=(ln(1.485))/(0.033)`

`t=12\ years`

1998+12=2010