SOLUTION: I am having a hard time answering the following problem. Any assistance would be much appreciated. Problem: The function f(t) = 9.7*e^(0.003*t)) models the population of a c

SOLUTION: I am having a hard time answering the following problem. Any assistance would be much appreciated. Problem: The function f(t) = 9.7e^(0.003t)) models the population of a c

Question 6507: I am having a hard time answering the following problem. Any assistance would be much appreciated.
Problem: The function f(t) = 9.7*e^(0.003*t)) models the population of a certain city f(t), measured in millions, t years after 1990. If the population growth rate continues into the future, when will the population reach 14 million?

Answer by Mike(39) (Show Source): You can put this solution on YOUR website!
sorry to butt in, but this is the wrong answer --> the f(t) is measured in millions of years, so f(t) is actually 14, not 14,000,000. Put 14 in the working, follow it through as below and you get t = 122.3 years, so in 1990+123 = 2113.
=============================================================================
In order to answer this problem, simply let the function equal to 14 million. In other words:
1) 14'000'000=9.7e^(0.003*t)
2) Divide by 9.7 on both sides: 1443298.969=e^(0.003*t)
3) Take the natural log of both sides to get rid of the e^: ln(1443298.969)=.003*t
4) Divide by .003 on both sides to give you the answer: t=4727.48 years
Hope this helps.
Regards,
-Mike
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