Anonymous
Anonymous asked in Science & MathematicsMedicine · 3 weeks ago

Drug question calculus?

A person enters a hospital for 24 hours and is given a drug. If t is in hours since the drug was administered, the concentration, in ng/ml, of a drug in the persons bloodstream is given by

C(t)=55te^-0.25t

The person is told complications can occur if they leave the facility and the concentration is above 4 ng/ml. Should the patient worry?

2 Answers

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  • 3 weeks ago

    No calculus is needed.  All we need to do is find the concentration when t=24 hours and see if it less than 4ng/ml.

    C(t)=55te^-(0.25t)

    C(24) = 55 * 24 * e^(-0.25*24) = 3.27 ng/ml

    So it is safe for the patient to leave aftewr 24 hours.

  • 4 = 55 * t * e^(-t/4)

    4/55 = t * e^(-t/4)

    https://www.wolframalpha.com/input/?i=4+%3D+55+*+t...

    t = 0.074

    t = 23.0316

    In either case, t < 24.  All we need to do now is find C(24)

    55 * 24 * e^(-24/4) =>

    110 * 12 * e^(-6) =>

    1320 / e^6 =>

    3.271952873199593118419621008678

    So we know that they're going to be fine.  We know that the only time the drug was ever at a dangerous concentration or higher was when they were at the facility and the drug is well below the dangerous threshold when they leave.

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