Results 1 to 12 of 12

Math Help - Rate of Change Word Problem

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    18

    Rate of Change Word Problem

    The rate of change of P with respect to h is proportional to p.

    p=3 when h=0

    p=2 when h=10

    p=? when h=50

    So far I know to take the derivative of P but I am terrible at word problems and don't know how to set up the equation. Any pointers would help. For example, I get confused when I see things like "with respect to". Any help at all would be appreaciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,887
    Thanks
    682

    Re: Rate of Change Word Problem

    Quote Originally Posted by Pewter12 View Post
    The rate of change of P with respect to h is proportional to p.

    assuming you meant the same "P" ...

    dP/dh = kP


    p=3 when h=0

    p=2 when h=10

    p=? when h=50

    So far I know to take the derivative of P but I am terrible at word problems and don't know how to set up the equation. Any pointers would help. For example, I get confused when I see things like "with respect to". Any help at all would be appreaciated.
    you are expected to know this basic differential equation has solution ...

    P = P_0 e^{kh}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2011
    Posts
    18

    Re: Rate of Change Word Problem

    Not sure if this matters but in my manual the first P is capitalized while the second is just lower case p.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,887
    Thanks
    682

    Re: Rate of Change Word Problem

    Quote Originally Posted by Pewter12 View Post
    Not sure if this matters but in my manual the first P is capitalized while the second is just lower case p.
    in a strict sense, they would not be the same variable, but, in order to solve the problem with the given information, they would have to be. I would assume the "manual" has a minor typo and both P's are one and the same variable.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2011
    Posts
    18

    Re: Rate of Change Word Problem

    Okay. I guess that makes sense. I still don't understand where the "k" variable comes from, however.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,887
    Thanks
    682

    Re: Rate of Change Word Problem

    Quote Originally Posted by Pewter12 View Post
    Okay. I guess that makes sense. I still don't understand where the "k" variable comes from, however.
    k is the constant of proportionality
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Sep 2011
    Posts
    18

    Re: Rate of Change Word Problem

    Nothing in my manual or text book even briefly alludes to any of this. . . is there any way of actually mathematically figuring the dp/dh=kp as the P=p0ekh at this level? I can't find any relevant examples and the solutions are not given in the text.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,887
    Thanks
    682

    Re: Rate of Change Word Problem

    Quote Originally Posted by Pewter12 View Post
    Nothing in my manual or text book even briefly alludes to any of this. . . is there any way of actually mathematically figuring the dp/dh=kp as the P=p0ekh at this level? I can't find any relevant examples and the solutions are not given in the text.
    what do you know about separable differential equations?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Newbie
    Joined
    Sep 2011
    Posts
    18

    Re: Rate of Change Word Problem

    I know that I am not sure what exactly separable differential equations are . . . I suppose I'm in way over my head.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,887
    Thanks
    682

    Re: Rate of Change Word Problem

    Quote Originally Posted by Pewter12 View Post
    I know that I am not sure what exactly separable differential equations are . . . I suppose I'm in way over my head.
    sound like you do not have the requisite knowledge to solve this problem.

    here is a link to an explanation ...

    Calculus Exponential Growth and Decay Word Problems
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Newbie
    Joined
    Sep 2011
    Posts
    18

    Re: Rate of Change Word Problem

    Thank-you!
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Newbie
    Joined
    Sep 2011
    Posts
    18

    Re: Rate of Change Word Problem

    Now that I have read the link and other relevant info from the site I fully understand the question!! Thank-you!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. word problem invovling rate change
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 12th 2010, 08:07 AM
  2. rate change word problem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 12th 2010, 01:59 AM
  3. rate change word problem
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: March 12th 2010, 01:59 AM
  4. word problem invovling rate change
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: March 11th 2010, 08:08 PM
  5. Rate of Change Word Problem
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 30th 2008, 01:14 PM

Search Tags


/mathhelpforum @mathhelpforum