2 polnts 1 Previous Answers SEssCacET2 4.3.04 My Notes Ask Your T A drug respons

Question

2 polnts 1 Previous Answers SEssCacET2 4.3.04 My Notes Ask Your T A drug response curve describes the level of medication in the bloodstream after a drug is administered. A surge function s) (where t> 0) is often used to model the response curve, refecting an initial surge in the djug level and then a more gradual decline. If, for a particular drug, A-0.02,p 4, k 0.03, and t is measured in minutes, estimate the times t corresponding irfiection points. (Round your answers to two decimal places.) X min (smaler value) t- min (larger value) Need Help

Explanation / Answer

S(t) = 0.02t^4*e^(-0.03t)

Find first derivative using product rule as

S'(t) =0.08 e^(-0.03 t) t^3 - 0.0006 e^(-0.03 t) t^4

Find second derivative using product rule as

S"(t) =e^(-0.03 t) t^2 (0.000018 t^2 - 0.0048 t + 0.24)

Now to find inflection point,

S"(t) =0

e^(-0.03 t) t^2 (0.000018 t^2 - 0.0048 t + 0.24) =0

hence using Quadratic formula

t= 66.67

t= 200

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