# Mathematics

A drug response curve describes the level of medication in the bloodstream after a drug is administered. A surge function
S(t) = At^(p)e^(−kt)
(where t > 0) is often used to model the response curve, reflecting an initial surge in the drug level and then a more gradual decline. If, for a particular drug, A = 0.01, p = 4, k = 0.08, and t is measured in minutes, estimate the times t corresponding to the inflection points. (Round your answers to two decimal places.)

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1. So, you have

s = 0.01 t^4 e^(-.08t)
s" = t^2 e^(-.08t)(.000064t^2-.0064t+.12)

so, there are inflection points at
t = 0, 25, 75

See the graph at

http://www.wolframalpha.com/input/?i=+0.01+t^4+e^%28-.08t%29+where+0%3C%3Dt%3C%3D100

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