Word problem help: exponential growth of population

[Guest]

I don't have alot but I always have trouble when it comes to word problems. Can you tell me if I have started correctly and if I have where I go from here. Thanks!! Andrea

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?

I have t= 2006 with P(sub0)=unknown
2000 is t-6=12,000
1990 is t-16=10,000.

Not sure where to go now.

 

[skeeter]

P₀ is the initial population at whatever time is called t = 0.

let 1990 be t = 0 ... P₀ = 10000

P = 10000e^kt

in 2000 (t = 10), P = 12000

12000 = 10000e^10k

1.2 = e^10k

ln(1.2) = 10k

k = ln(1.2)/10 ... you now have a value for k.

solve the following equation for t to complete the problem.

20000 = 10000e^kt