Results 1 to 3 of 3

Math Help - Exponential Differentiation

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    15

    Lightbulb Exponential Differentiation

    In studying salmon populations, a model often used is the Ricker equation which relates the size of a fish population this year,
    x to the expected size next year y. (Note that these populations do not change continuously, since all the parents die before the eggs are hatched.) The Ricker equation is
    y = axe^(-bx) where a,b> 0
    Find the value of the current population which maximizes the salmon population next year according to this model.

    ---> I differentiated it this far:
    dy/dx = axe(-bx)(-b) + e^(-bx)(a)
    dy/dx = -axe^(-bx)b + ae^(-bx)
    dy/dx = 0 = ae^(-bx) (-xb + 1)

    in the question we are given that a,b>0 Could anyone please tell me how to further solve this question??

    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426
    Quote Originally Posted by ninja View Post
    in studying salmon populations, a model often used is the ricker equation which relates the size of a fish population this year,
    x to the expected size next year y. (note that these populations do not change continuously, since all the parents die before the eggs are hatched.) the ricker equation is
    y = axe^(-bx) where a,b> 0
    find the value of the current population which maximizes the salmon population next year according to this model.

    ---> i differentiated it this far:
    dy/dx = axe^(-bx)(-b) + e^(-bx)(a)
    dy/dx = -abxe^(-bx) + ae^(-bx)
    dy/dx = 0 = ae^(-bx) (-bx + 1)

    \textcolor{red}{x = \frac{1}{b}}

    ...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2009
    Posts
    15
    Quote Originally Posted by skeeter View Post

    ...
    i was just doing something wrong in the second derivative (to prove max) due to which it was turning out be a minimum. thanks anyways for spending your time on it.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. exponential differentiation.
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 11th 2010, 08:02 AM
  2. exponential differentiation
    Posted in the Calculus Forum
    Replies: 5
    Last Post: May 12th 2009, 03:30 PM
  3. exponential differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 12th 2009, 01:52 AM
  4. Differentiation of exponential
    Posted in the Calculus Forum
    Replies: 9
    Last Post: October 9th 2008, 03:57 PM
  5. exponential differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 3rd 2007, 09:19 AM

Search Tags


/mathhelpforum @mathhelpforum