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Rate of change of fish population.

  1. Jul 18, 2011 #1
    1. The problem statement, all variables and given/known data

    The population of a species of fish is given by the equation below. Where t is time in years. What is the rate of change of the fish population after 5 years?

    2. Relevant equations

    P(t)= 1.2 x 10^8(1+0.02t)^ -2 where t is time in years


    3. The attempt at a solution

    Before i go further i just want to know if i am setting it up right from the beginning, here is how i started:

    P'(t) = 1.2x10^8(1/sqrt of 1+0.02t)
    = 1.2x10^8/sqrt of 1+0.02t
     
  2. jcsd
  3. Jul 18, 2011 #2

    tiny-tim

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    Last edited by a moderator: Apr 26, 2017
  4. Jul 18, 2011 #3
    that big sci fi constant in front of the brackets messes me up when i try to use the chain rule for some reason, did i do this right to start?
    (-2)(1.2x10^8)(1+0.02t)^-3(0.02)
     
  5. Jul 18, 2011 #4

    tiny-tim

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    (-2)(1.2x108)(1+0.02t)-3(0.02) ?

    yes, that's correct :smile:
     
  6. Jul 18, 2011 #5
    okay, i think i might be doing the order wrong though from here, here is what i got next:

    P'(t) = -2.4x10^8(0.02)(1+0.02t)^-3
    = -4.8x10^6(1+0.02t)^-3 this doesn't look right to me somehow?
     
  7. Jul 18, 2011 #6

    tiny-tim

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    why?? :confused:
     
  8. Jul 18, 2011 #7
    Actually, i take that back as it appears when i plug the 5 years into the expression it works out to be the correct answer. so thank you all is well.
     
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