SOLUTION: The population of a city is given by P=5000e^kt where t is time in years, with t=0 coresponding in year to 2000. In 1990 the population was 34,500. Find the value of k and predict

Question 35368This question is from textbook
: The population of a city is given by P=5000e^kt where t is time in years, with t=0 coresponding in year to 2000. In 1990 the population was 34,500. Find the value of k and predict the population in 2030.
I come up with 123,608 if I use the negative in my problem
34,500 =5000e^k(-10)
6.9 = e^k(-10)
ln6.9 = k(-10)
P= 5000e^(-.193152141)(30)
P= 123,608 population in 2030
Is this correct??? Thinking it should be higher This question is from textbook

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The population of a city is given by P=5000e^kt where t is time in years, with t=0 coresponding in year to 2000. In 1990 the population was 34,500. Find the value of k and predict the population in 2030.
I come up with 123,608 if I use the negative in my problem
34,500 =5000e^k(-10)
6.9 = e^k(-10)
ln6.9 = k(-10)
P= 5000e^(-.193152141)(30)
P= 123,608 population in 2030
Is this correct??? Thinking it should be higher
I think it is smaller than that.
In 1990 the population was 34,500
In 2000 the population was only 5000
This is a decreasing population.
The negative is correct but your exponent is not; you need to include
the "30" in the exponent.
Try P = 5000e^(-0.193152141*30)= 15 people.
Cheers,
Stan H.
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