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anonymous
 5 years ago
A population grows according to the equation P(t) =60005500e^(0.159t) for t>0 or t=0, t measured in years. This population will approach a limiting value as time goes on. During which year will the population reach HALF of this limiting value?
anonymous
 5 years ago
A population grows according to the equation P(t) =60005500e^(0.159t) for t>0 or t=0, t measured in years. This population will approach a limiting value as time goes on. During which year will the population reach HALF of this limiting value?

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What is the limit as t goes to infinity of e^0.159t?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So what does P(t) go to as t goes to infinity?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Since e^0.159t goes to 0, 5500e^(0.159t) goes to zero as well, right. It's just 5500(0).

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0What happens to the 6000?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Since that second part goes to zero, you have 60000 which is just 6000. That's the limiting value

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Okay so I basically just take the limit of each parts 6000 and 5500e^(0.159t) and I end up with 6000 for the limiting value.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Thank you! Do you know how to do the second part?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0You know the limiting value. So half of that is 3000. So P(t)=3000, you need t. So 3000=60005500e^(0.159t). Isolate e^(0.159t) then take the natural log of both sides.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So just simply solve for t?

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Yeah. They are asking for the time the population will be 3000.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0I know how to do it know! Thanks a lot!
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