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Math Help - Can anyone solve this using reccurance relation!!!!!

  1. #1
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    Can anyone solve this using reccurance relation!!!!!

    1. A nuclear reactor has created 18 grams
    of a particular radioactive isotope. Every
    hour 1% of a radioactive isotope decays.

    a) Set up a recurrence relation for the
    amount of thus isotope left after
    n

    hours.

    b) What are the initial conditions for the
    recurrence relation in part (a)?

    c) Solve this recurrence relation.
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  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
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    Hello, Jay dee!

    This one is quite simple . . .


    1. A nuclear reactor has created 18 grams of a particular radioactive isotope.
    Every hour 1% of a radioactive isotope decays.

    a) Set up a recurrence relation for the amount of thus isotope left after n hours.
    a_n \;=\;0.99 a_{n-1}


    b) What are the initial conditions for the recurrence relation in part (a)?
    a_0 = 18


    c) Solve this recurrence relation.
    a_n \;=\;0.99^n(18)

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