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Rate of Change Derivitive

  1. Feb 24, 2012 #1
    1. The problem statement, all variables and given/known data
    A population of 500 bacteria is introduced into a culture and grows in number according to the equation P(t)=500(1+(4t/(50+t2), where t is measured in hours. Find P'(2), an interpret the results.

    2. Relevant equations

    3. The attempt at a solution
    I used the product rule, sum and difference rule, and the quotient rule, but it seems like I used it a lot and there is a lot of steps that I used. I think I am over-thinking this problem. But I got 10000-200t2/(50+t2)2
  2. jcsd
  3. Feb 24, 2012 #2


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    Is it supposed to be this?
    [tex]P(t) = 500\left( 1 + \frac{4t}{50 + t^2}\right)[/tex]
    I also got something different for P'(t).
  4. Feb 24, 2012 #3


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    hi cdoss! :smile:
    where is there a product? i only see a quotient :confused:

    show us your full calculations :smile:
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