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Silly modeling question

  1. Feb 26, 2009 #1
    o my bro ahd an algebra 2 midterm and a question was this:

    ) A printer costs $35,000 (how old are these questions lol) but it depreciates 5% a year. What is the value by the 4th year?

    ok so being an overtly complex person i tried to model a differential equation of this just for the kicks.

    At first I thought

    dP/dt=-0.05P

    where P is price

    and the solution is Po*exp(-0.5t) where Po=35000

    however this is wrong. So I assumed I did not know r from dP/dt=-rP and worked the problem by finding the initial values.

    so the solution gives me P=exp(-.051293t)Po which is correct.

    I dont grasp intuitively the answer. why is dP/dt=.051293P when the problem says it goes down 0.5 each year so I assume P changes over time by -0.05P per year?
     
  2. jcsd
  3. Feb 27, 2009 #2
    P does change by 0.5 per year. Look up continuously compounded interest vs annually compounded interest.

    http://en.wikipedia.org/wiki/Compound_interest
     
    Last edited: Feb 27, 2009
  4. Feb 27, 2009 #3
    That's weird. Where did my posts go? I swear I answered this question already...
     
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