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Calculus

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The amount A in grams of radioactive plutonium remaining in a 20-gram sample after t days is given by the formula A=20*(1/2)^(t/140). At what rate is the plutonium decaying when t=2 days?

  • Calculus - ,

    Given
    A(t)=20(1/2)^(t/140)
    We look for A'(t)

    Use implicit differentiation.

    Take ln on both sides
    ln(A)=ln 20 + (t/140)ln(1/2)
    differentiate with respect to t
    (1/A)dA/dt = 0 + ln(1/2)/140
    substitute A
    dA/dt = ln(1/2)/140*20(1/2)^(t/140)
    substitute -ln(2) for ln(1/2)
    dA/dt = -(ln(2)/7)*(1/2)^(t/140)

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