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Differential Equation (Deposit)

  1. Dec 6, 2009 #1
    1. The problem statement, all variables and given/known data

    A person initially place $500 in a saving account that pays interest at the rate of
    4% per year compounded continuously. Suppose the person arranges for $10 per
    week to be deposited automatically into the savings account.
    (I) Write a differential equation for P (t), the amount on deposit after t years
    (assume that “weekly deposits” is close enough to “continuous deposits” so
    that we may model the balance with a differential equation.)


    2. Relevant equations

    Let X(t) be the amount on deposit after t years and dX/dt be the rate of change of the deposit.

    3. The attempt at a solution

    dX/dt = 0.04X +480 (480 is the amount of deposit yearly)
    and
    X(t) = C e^0.04t +480t , where C is a constant

    Let X(0) = C =500, then
    P(t)=500e^0.04t+480t

    Acturally, I dun no the approach is correct or not? Pls Help!
     
  2. jcsd
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