Inflection Points

Question

A  response curve describes the level of medication in the bloodstream after a drug is administered. A surge function S(t) = At^pe^−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 = 0.02, p = 4, k = 0.07, and t is measured in minutes, estimate the times t corresponding to the inflection points. (Round your answers to two decimal places.)

t =		min (smaller value)
t =		min (larger value)

Answer 1

set second derivative S''(t)=0

using just symbols for S''(t) setting to zero, dividing out Ae^-kt

and the letting p=4

find want

k²t⁴-8kt²+12t²=0,,,,divide out t² and have quadratic

t=(4/k)+/-(2/k)

inflection points at t=28.5 and 85.5 minutes approximately.