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Math Help - rates and related rates

  1. #1
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    rates and related rates

    An item costs $600 at time t = 0 and costs $P in year t. When inflation is r% per year, the price is given by the following equation.
    P = 600e^(rt/100)
    (a) If r is a constant, at what rate is the price rising (in dollars per year) initially?

    At what rate is the price rising after 2 years?

    (b) Now suppose that r is increasing by 0.3 per year when r = 4 and t = 2. At what rate (dollars per year) is the price increasing at that time?

    i would appreciate some quick help here please...thanks
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by mathaction View Post
    An item costs $600 at time t = 0 and costs $P in year t. When inflation is r% per year, the price is given by the following equation.
    P = 600e^(rt/100)
    (a) If r is a constant, at what rate is the price rising (in dollars per year) initially?

    At what rate is the price rising after 2 years?
    First for constant r we need:

    <br />
\frac{dP}{dt}=600~\frac{r}{100}~e^{rt/100}<br />

    Then when t=0 we have the initial rate of increas in price is:

    <br />
\left. \frac{dP}{dt}\right|_{t=0}=600~\frac{r}{100}~e^{r(  0)/100}=6r \mbox { dollars per year }<br />

    After 2 years we have:

    <br />
\left. \frac{dP}{dt}\right|_{t=2}=600~\frac{r}{100}~e^{r(  2)/100}=6r e^{r/50} \mbox { dollars per year }<br />

    RonL
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by mathaction View Post
    An item costs $600 at time t = 0 and costs $P in year t. When inflation is r% per year, the price is given by the following equation.
    P = 600e^(rt/100)
    (a) If r is a constant, at what rate is the price rising (in dollars per year) initially?

    At what rate is the price rising after 2 years?

    (b) Now suppose that r is increasing by 0.3 per year when r = 4 and t = 2. At what rate (dollars per year) is the price increasing at that time?

    i would appreciate some quick help here please...thanks
    For non-constant r we have:

    <br />
\frac{dP}{dt}= 6 r e^{rt/100}~ \frac{dr}{dt}<br />

    Now just insert the values to get the answer.

    RonL
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