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6 March, 01:52

The quantity of a drug in the bloodsteam t hours after a tablet is swallowed is given, in mg, by q (t) = 40 ((e^-t) - (e^-2t))

What is the maximum amount of the drug in the bloodstream at one time?

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  1. 6 March, 02:19
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    Q (t) = 40 ((e^-t) - (e^-2t))

    For q (t) to be maximum dq/dt = 0

    dq/dt = 40 ( - (e^-t) + 2 (e^-2t) = 0

    2e^-2t - e^-t = 0

    2e^-2t = e^-t

    e^t = 2

    t = ln 2

    q (ln 2) = 40 ((e^ (-ln 2) - (e^ (-2ln 2)) = 40 (1/2 - 1/4) = 40 (1/4) = 10

    Therefore, thw maximum amount of drug in the bloodstream at one time is 10 mg.
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