The population of a midwestern city follows the exponential law. If the population decreased from 900,000 to 800,000 from 1993 to 1995, what will the population be in 1997?
Extra: What is the population in 2008?
$\displaystyle P = P_0 e^{kt}$ where t is number of years measured from start of 1993.
At t = 0, P = 900,000 therefore $\displaystyle P_0 = 900,000$ and so $\displaystyle P = 900,000 e^{kt}$.
Substitute t = 2, P = 800,000 and solve for k:
$\displaystyle 800,000 = 900,000 e^{2k} \Rightarrow \frac{8}{9} = e^{2k} \Rightarrow \ln \frac{8}{9} = 2k \Rightarrow k = $ .... (I'd suggest getting an answer correct to five decimal places).
Now substitute the values of t corresponding to 1997 and 2008 and solve for P in each case.