algebra 4

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write an exponential decay model that describes the situation.

one hundred grams of plutonium is stored in a container.the amount p (in grams) of plutonium present after t years can be modeled by this equation.

p=100(0.99997)t

hpw much plutonium is present after 20,000years

  • algebra 4 -

    you have a typo I think
    The idea is that the amount lost per unit time is proportional to the amount present at each time
    dp/dt = -k p
    dp/p = -k dt
    ln p = -kt
    constant*p = e^(-kt)
    find the constant when t = 0 so e^-kt = 1
    p = 100 at t = 0
    p = 100 e^-kt
    so what you probably meant to type was that with k = .99997
    so
    p = 100e^-(.99997*20,000)
    p = 0 on my calculator after 20,000 years

  • algebra 4 -

    or the equation was given as

    p = 100(.99997)^t

    for t = 20000, my calculator gave me
    p = 54.88 g

    As Damon pointed out, your equation as it stands makes little sense.

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