Since constants are generally placed as coefficients, I'll write
S(t) = Apte^(−kt)
S'(t) = Ap(1-kt)e^(-kt)
S"(t) = Apk(kt-2)e^(-kt)
Inflection points occur where S"=0, so we have
0.0056(0.07t-2)e^(-.07t) = 0
This is at t = 2/.07 = 28.57
There is only one inflection point
So that make me think you meant to type
S(t) = At^p e^(-kt) = 0.02t^4e^(-.07t)
S'(t) = t^3(0.08-0.0014t)e^(-.07t)
S"(t) = t^2(0.0098t^2-0.0112t+0.24)e^(-.07t)
S'=0 at t=200/7, 600/7
A drug response curve describes the level of medication in the bloodstream after a drug is administered. A surge function
S(t) = Atpe−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)
1 answer