Question 50196: 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.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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
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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.
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