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Exponential growth

  1. Mar 14, 2010 #1
    The problem statement, all variables and given/known data
    To encourage buyers to place 100-unit orders, your firm's sales department applies a continuous discount that makes the unit price a function p(x) of the number of units x ordered. The discount decreases the price at a rate of $0.01 per unit ordered. The price per unit for a 100-unit order is p(100) = $20.09. Find p(x) by solving the following initial value problem:

    Differential equation: dp/dx = -p/100
    Initial condition: p(100) = 20.09


    The attempt at a solution
    So I integrated the differential equation and applied the initial condition to it. I was able to get the following equation:

    [tex]p = 20.09e^{1 - x/100}[/tex]

    Is this correct?
     
    Last edited: Mar 14, 2010
  2. jcsd
  3. Mar 14, 2010 #2

    jbunniii

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    Yes, it's correct. You can verify it by confirming that it satisfies the differential equation and the initial condition.
     
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