Question 874689: Click here to see ALL problems on Miscellaneous Word Problems
Question 874204: A city has been declining in population for the last 50 years.
I have not learned the number e yet, or ln. The answer I was given to this question did not make sense to me. :(
Please help me again!
In the year 2000, the population was 571 thousand, and was declining at a rate of 0.77% per year. If this trend continues:
(A) Give a formula for the population of this city, P, in thousands, as a function of t, the number of years since 2000.
P=
(B) What is the predicted population in 2010?
The predicted population is thousand people.
(C) To two decimal places, estimate t when the population is 450 thousand people.
When there are 450 thousand people in this city, t≈
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website! A) P(t) = P0*e^rt, where P(t) is population at time t, r is the rate, t is time in years
B)r= -0.0077, t = 10, e = 2.71828
P(10) = 571,000*e^(-0.0077)10
P(10) = 528,683
C)450000 = 571000*e^(-0.0077)t
450000/571000 = e^(-0.0077)t
0.7880 = e^(-0.0077)t
(-0.0077)t = ln (0.7880)
(-0.0077)t = −0.2383
t = 30.95 years
When there are 450 thousand people in this city, t≈ 30.95 years
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