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Math Help - Help on Exponential Growth/Decay Question

  1. #1
    RodddersPrime
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    Question Help on Exponential Growth/Decay Question

    Hi guys, I am doing A-levels and I came across two question I need help with.

    We are told the exponential equation is P= ab^t
    P=Quantity
    a= initial value
    b=constant indicating how fast the quantity is growing
    t=time
    Question 1)
    A radioactive substance decays at rate of 12% per hour
    a)Find after how many hours half of the radioactive material will be left.
    b) How many hours did it have twice the current amount of radioactive material?
    I know all but one value for the equation P= ab^-t, which is a. How Do I know the initial value of this substance?

    Question 2)
    A dangerous radioactive substance has a half life of 90 years. It will be deemed safe when its activity is down to 0.005 of it's initial value. How long before it's deemed safe?
    I have no idea how to do this one.

    Thanks in advance.
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by RodddersPrime View Post
    I know all but one value for the equation P= ab^-t, which is a. How Do I know the initial value of this substance?
    You don't need to. Postulate an initial amount of your substance, say N. Then for the first part you want to find out how long it takes for only half to be left, so your amount of substance is (1/2)N. The N's cancel.

    -Dan
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  3. #3
    Forum Admin topsquark's Avatar
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    Question 2)
    A dangerous radioactive substance has a half life of 90 years. It will be deemed safe when its activity is down to 0.005 of it's initial value. How long before it's deemed safe?
    The activity of a substance is the number of decays per second. This will be proportional to the amount of the substance you have, so you again have the same equation:
    A = A_02^{-t}
    that you can use.

    In this case you will have A = 0.005A_0.

    -Dan
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