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Derivative of P(x) = 0.2 -0.125e^(0.005x) for X=1

  1. Apr 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Derivative of P(x) = 0.2 -0.125e^(0.005x) for X=1
    P(x) is the population in Millions and X is the year where 0 = 2000
    I have to explain the answer I am getting at the end.
    2. Relevant equations

    3. The attempt at a solution
    d/dx (0.2 -0.125e^(0.005x))
    I find -0.000625*(1,00501)^x // did this with my calculator
    -0.000625*(1,00501)^1 = -0.000628

    does that simply mean that the population is going down over time?
  2. jcsd
  3. Apr 9, 2015 #2
    Welcome to PF,
    Great work, just want to point at something, P(x) = 0.2 -0.125*e^(0.005)
    It has a something constant - some exponontial, so it will be decreasing so fast over the years,
    Hope i've helped,
    [Edit: To answer, you have to write down the derevative of P in terms of x, and what should it's sign be to be decreasing ?]
  4. Apr 9, 2015 #3


    Staff: Mentor

    I don't know what you entered into your calculator, but it came out wrong. The derivative should involve e raised to the power kx.

    I would advise putting your calculator away and doing this by hand. You're more likely to get the right answer.
  5. Apr 9, 2015 #4
    Thats because my calculator calculated e^0.005*x = 1.00501^x
  6. Apr 9, 2015 #5
    Yeah I wrote down the derevative of P in terms of x and I believe that since its negative the population is decreasing ?
  7. Apr 9, 2015 #6
    Yepp, great work .
  8. Apr 9, 2015 #7
    thanks awesome.

    This forums makes me like University even more :) I love school & studying :)
  9. Apr 9, 2015 #8


    Staff: Mentor

    Operator error

    To make that calculation, you need parentheses, as in e^(.005*x).
  10. Apr 9, 2015 #9


    Staff: Mentor

    Please pay closer attention before making comments about the correctness of a poster's work. The OP made a gross error in his first post, which you apparently didn't notice.
  11. Apr 9, 2015 #10
    oh ok thank you very much :)
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