SOLUTION: 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 Th

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
-------------
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.
RELATED QUESTIONS
Hello, I always have trouble with word problems and I just want to make sure that I am (answered by Theo)

Hello, I have problems with word problems and I always have. Now I am in Algebra I and... (answered by josmiceli)

Ratio and Proportion 1. A lawyer bills her clients $200 per hour of service. If a... (answered by stanbon)

Hi! I usually get very confused when it comes to linear graphs and so I remember how to... (answered by solver91311)

Ben is making wooden toys for the next arts and crafts sale. Each toy costs Ben $1.80 to... (answered by ankor@dixie-net.com)

I have trouble with negative word... (answered by Alan3354)

I am unclear as to how to put this problem together: To estimate the population of... (answered by stanbon)

3x+4>1/3 (x-2) I always have trouble when i comes to fractions. Here's what I have so (answered by vleith)

I don't have any idea how to do these word problems. I've been trying but I just don't... (answered by KnightOwlTutor)