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

Answer:

In the year 2010

Step-by-step 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

$ln(e)=1$

$ln(1.485)=(0.033t)$

$t=\frac{ln(1.485)}{0.033}$

$t=12\ years$

1998+12=2010