## anonymous one year ago 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.

1. anonymous

my answer 2005 what my teacher said Substitute the values given to find the final answer. t is years after 1998 so once you have t add this to the year 1998.

2. anonymous

thats what i thought

3. phi

$114 e^{0.024t} = 140 \\ e^{0.024t} = \frac{140}{114} \\ 0.024 t = \ln\left(\frac{140}{114} \right) \\ t= \frac{\ln\left(\frac{140}{114} \right) }{0.024}$

8.56

5. phi

t= 8.56 years add this to 1998

6. phi

you get 2006.56 which is the middle of 2006