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Math Help - Can someone help me with this expoential decay problem?

  1. #1
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    Can someone help me with this expoential decay problem?

    "Suppose a radioactive substance decays at a rate of 3.5% per hour. What percent of the substnce is left after 6 hours?"
    Can you please list what I would have to do to solve this problem?
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  2. #2
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    Re: Can someone help me with this expoential decay problem?

    Hey EJdive43.

    Does it decay continuously or only in hourly intervals?
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  3. #3
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    Re: Can someone help me with this expoential decay problem?

    Hello, EJdive43!

    A radioactive substance decays at a rate of 3.5% per hour.
    What percent of the substance is left after 6 hours?

    First, set up the function.

    The substance loses 3.5% every hour.
    That is, 96.5% of the substance remains.

    We have: . P \:=\:P_o(0.965)^t . where \begin{Bmatrix} P_o &=& \text{original amount} \\ t &=& \text{time (in hours)} \end{Bmatrix}

    When t = 6, we have: . P \:=\:P_o(0.965^6)

    . . . . . . . . . . . . . . . . . P \:=\:P_o(0.807539696)

    . . . . . . . . . . . . . . . . \frac{P}{P_o} \:=\:0.807539696

    Therefore: . \frac{P}{P_o} \;\approx\;80.75\%
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