What is the expansion rate of the population?

Question

The population of Cedar Rapids is expanding at a rate of
P = Po e^kt,
where Po 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?

Answer 1

Look at the data from 1990 and 2000. We have P in 2000 equal to 12000, and Po in 1990 equal to 10000, with t = 10 years between 1990 and 2000. Therefore, 12000 = 10000e^(10k). Now k is your only unknown, and you can solve for it.

12000 = 10000e^(10k)
1.2 = e^(10k)
ln(1.2) = 10k
k = (ln(1.2))/10
k ~= 0.018

We are looking for a population of 20000. So now we set P = 20000 and use Po of 10000 again, but this time t is our unknown. Just solve 20000 = 10000e^(0.018t) for t using the method above, and add the result to 1990.

Answer 2

really fast...Were multiplying like rabbits...