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Math Help - Problem solving

  1. #1
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    Problem solving

    I just want to make sure that I got the right answer.


    that's how I found A since, C is the limit I plugged 100,000 for it. B is the growth rate and it's 1 as mentioned. now to find a, I just plugged it the initial pop when time was 0.
    100=100,000/(1+ae^-0*1)
    100(a+1) = 100,000
    100a +100 = 100,000
    100a = 99,900
    a=99,900/100
    a= 999
    therefore, the final equation is
    p(t) = 100,000/(1+999e^-t)

    just want to make sure that I got it right, thx for your help.
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  2. #2
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    Quote Originally Posted by melvis View Post
    I just want to make sure that I got the right answer.


    that's how I found A since, C is the limit I plugged 100,000 for it. B is the growth rate and it's 1 as mentioned. now to find a, I just plugged it the initial pop when time was 0.
    100=100,000/(1+ae^-0*1)
    100(a+1) = 100,000
    100a +100 = 100,000
    100a = 99,900
    a=99,900/100
    a= 999
    therefore, the final equation is
    p(t) = 100,000/(1+999e^-t)

    just want to make sure that I got it right, thx for your help.
    Take the limit as t goes to infinity.
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  3. #3
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    Quote Originally Posted by dwsmith View Post
    Take the limit as t goes to infinity.
    It stays at 100,000 where it should stay ? I'm assuming that's a way to check this kind of problem, right?
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  4. #4
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    Correct.
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  5. #5
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    Quote Originally Posted by melvis View Post
    It stays at 100,000 where it should stay ? I'm assuming that's a way to check this kind of problem, right?
    It says the island can hold no more than 100,000 so you are correct or made an error that yields the same results. The odds are in your favor on being correct though.
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  6. #6
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    Thx for the help .

    Quote Originally Posted by dwsmith View Post
    It says the island can hold no more than 100,000 so you are correct or made an error that yields the same results. The odds are in your favor on being correct though.
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  7. #7
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    Quote Originally Posted by melvis View Post
    Thx for the help .
    Your welcome. Whenever you know the maxium number whether it be population, bacteria, etc, you can take the limit as t,x, ... goes to infinity. It would be extremely rare that a mistake will allow you to obtain the correct limit.
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