Question

The formula A = 118e0.024t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 140 thousand? Show your work.

Answer 1

Answer:2006

Step-by-step explanation:

$A = 118e^{0.024t}$

When A = 140:

$140 = 118e^{0.024t}$

$\frac{140}{118} = e^{0.024t}$

$ln(\frac{140}{118}) = 0.024t$

$\frac{1}{0.024} ln(\frac{140}{118}) = t$

Plugging into a calculator, t is approximately 7.12.  Since t represents years since 1998, we round up to the nearest whole number: t=8.  So the population of the city will reach 140 thousand in the year 2006.