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!

Differential eq problem

  1. Oct 18, 2005 #1
    Differential eq problem (urgent)

    I have the following question which I was to answer:
    "The rate of increase of the rate of inflation is decreasing". Write this sentence in terms of derivatives of average prices.

    My answer was:
    Let p=price
    t=time
    Therefore rate of change of price = dp/dt (Inflation) = I

    Therefore rate of change of Inflation = I'

    Therefore I'= (d^2p)/(dt^2)

    Since the rate of change of Inflation is decreasing;

    I' = - (d^2p)/(dt^2)

    I just wanted to check whether my answer is correct.
    Please help.
     
  2. jcsd
  3. Oct 19, 2005 #2

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    So far, so good.

    Your answer is not correct, and if you look at two of your lines side by side it should be clear why:

    If I' simultaneously equals both (d^2p)/(dt^2) and - (d^2p)/(dt^2), then I' can only be zero, which is obviously not true.

    Your first definition of I' is correct. So, if I is decreasing then what mathematical statement would you say about I'?
     
  4. Oct 20, 2005 #3
    So if dI/dt is decreasing, is the I' negative? (i.e. -I')?
     
  5. Oct 20, 2005 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Actually, if I read this correctly, there is another problem that has not been addressed:
    "The rate of increase of the rate of inflation is decreasing"

    Yes, the "rate of inflation" is dp/dt. Yes, the "rate of increase of the rate of inflation" is d2p/dt2. Now you want say that that is decreasing. What must be true of its derivative (i.e. d3p/dt3?
     
  6. Oct 20, 2005 #5

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    No, you're just making the same mistake all over again. If I'=-I', then I' can only be zero.

    Think about it, if you want to say that x is negative then you don't say that x is -x, you say that x is less than zero.

    So how do you write that down in mathematical symbols?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?