Pre Calc!

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A drug is eliminated from the body through urine. Suppose that for a dose of 10 milligrams, the amount A(t) remaining in the body t hours later is given by A(t)=10(0.8)^t and that in order for the drug to be effective, at least 2 milligrams must be in the body.

(a) Determine when 2 milligrams is left in the body.

(b) What is the half-life of the drug?

  • Pre Calc! -

    a)
    A(t)=A0(0.8)^t
    For 2 mg left, we have A(t)=2, A0=10, so
    2=10(0.8)^t
    0.8^t = 1/5
    take ln on both sides,
    t*ln(0.8)=ln(1/5)
    t=ln(0.2)/ln(0.8)
    =7.2 hours

    b)
    Half-life is the time it takes to reduce the quantity to 0.5A0, i.e.
    5=10(0.8)^t
    solve for t similar to a) above.

  • Pre Calc! -

    Thank you!

  • Pre Calc! -

    You're welcome!

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