1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Application of diffentation

  1. May 14, 2014 #1
    1. The problem statement, all variables and given/known data
    can anyone expalin where to get the equation for max growth? and the value? this is not my working. this is just the sample ans.


    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. May 14, 2014 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You get it from the equation of the growth.
     
  4. May 14, 2014 #3
    which is the equation? so confused now.
     
  5. May 14, 2014 #4

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Derived as part of the answer to part (a), used in part (b).
    The whole question is about you ability to turn words into equations and vise versa.
    Consider: what does "rate of population growth" mean?

    Here is your question:
    Q8. A territory will support a maximum population of ##P_0##. Let the ratio of the population ##P## to the maximum population be ##p##... the rate of change of this ratio is the product of ##p## and the difference between ##p## and ##1##.

    (a) write down the differential equation in ##p##
    (b) show that the growth of the population is greatest when ##P=\frac{1}{2}P_0##
    (c) the population starts at ##\frac{1}{4}P_0## and reaches ##\frac{1}{2}P_0## in 20 years.
    Find the time for the population to reach ##\frac{7}{8}P_0##.
    (d) find the value of ther maximum growth of the population to 3dp.
     
  6. May 15, 2014 #5

    pasmith

    User Avatar
    Homework Helper

    Vital omission corrected.
     
  7. May 15, 2014 #6

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Does your text really say "defferential equation"? That makes me wonder about the grammar- and, in particular, whether "maximum growth" means the maximum population or maximum rate of growth of the population. If it is "maximum rate of growth", (b) asks you to "show that the growth of the population is greatest when [itex]P= \frac{1}{2}P_0[/itex]". What is the rate of growth then?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Application of diffentation
  1. Implicit applications (Replies: 16)

Loading...