A model for the concentration of an antibiotic drug in the bloodstream t hours after the administration of the drug is C(t) = 2.5(e^(-0.3t) - e^(-0.7t)) where C is measured in µg/mL. (a) At what time does the concentration have its maximum value? What is the maximum value? (b) At what time does the inflection point occur? What is the significance of the inflection point?
Added by Donald M.
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The derivative of C(t) is C'(t) = 2.5(-0.3e^(-0.3t) + 0.7e^(-0.7t)). Setting this equal to zero and solving for t gives t = ln(7/3) / 0.4 ≈ 1.45 hours. Substituting this into the original equation gives the maximum concentration as C(1.45) ≈ 0.92 µg/mL. (b) The Show more…
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