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Exponential growth of populations (Q=Ae^kt)

  1. Apr 28, 2007 #1
    1. The problem statement, all variables and given/known data
    The number of rabbits in a colony is given by N=80e^(0.02t) where t is in days.
    c) After how many days will there be 500 rabbits?


    2. Relevant equations
    (ln being the exponential logarithm)
    and possibly the conversion formula: ln y = x --> y=e^x

    3. The attempt at a solution

    what i tried was coverting Q=Ae^kt to A ln Q=kt
    Then divided both sudes by x to give:

    A ln Q = t

    Which after substitution looked like this:

    80 ln 500 = t

    Which gave t=24,858 days.
    where as the answer is 92 days... :grumpy:
    Last edited: Apr 29, 2007
  2. jcsd
  3. Apr 28, 2007 #2


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    This equation is wrong. Perhaps you are getting confused with your variables; there's no reason to introduce x, stick with A, k and t and try again.
  4. Apr 29, 2007 #3
    Yeah i ment k not x.
    in my maths book in the examples it has x. but it still doesnt work with k in there... :frown:
  5. Apr 29, 2007 #4


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    Start by dividing both sides by 80, so you isolate the exponent part. From there it might seem easier.
  6. Apr 29, 2007 #5
    i dont know how dividing both sides by 80 will make it easier or alter the answer in any way...
    i want to know if there is a problem with my working. im not sure if it is even the right formula...
  7. Apr 29, 2007 #6


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    If you really believe that using the letter "x" gives you a different equation that using the letter "k", you need to review basic algebra!

    You have already been told that there is a problem with your "working"!

    You are given the formula [itex]N= 80e^{0.02t}[/itex] so of course, that the correct formula. You are also told that N= 500 so the equation you want to solve is [itex]80 e^{0.02t}= 500[/itex]. Surely, it would be an obvious first step to divide both sides by 80? After you have done that take the natural logarithm of both sides.
  8. May 2, 2007 #7
    ok got it.
    500 = 80e^0.02t
    goes to
    ln 6.25 = t
  9. May 2, 2007 #8


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    Okay, now, what is your answer to the question?
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