Question 50196
The population of Cedar Rapids is expanding at a rate of P = P(sub0)e^kt,
where P(sub0) is the current population, k is the expansion rate and t is time (in years). If the populations were 10,000 in 1990 and 12,000 in 2000, when will it reach 20,000? 
--------------------------
P(t)=P(0)e^kt
In ten years the population increased from 10000 to 12000, so:
12000=10000e^k(10)
1.2=e^(10k)
Take the natural log of both sides to get:
10k = ln1.2
10k= 0.18
k=0.018
-------------
Now you can rewrite the general equation as follows:
P(t)=P(0)e^(0.018t)
20000=10000e^(0.018t)
2=e^0.018t
ln2=0.018t
t=0.693147.../0.018
t=38.5 years

The 10000 corresponds to the year 1990
38.5 years later will be 2029 when the population will be 20000
Cheers,
Stan H.