A drug response curve describes the level of medication in the bloodstream after a drug is administered. A surge function Solution dS/dt = d(Atpe-kt)/dt = Atp(-k)e-kt+Ae-kt(ptp-1) = Ae-kttp-1(-kt+p) Since A, e-kt, tp-1 are positive (t>0) S is decreasing when dS/dt is negative when (-kt+p)<0 or t > p/k S is increasing when dS/dt is positive when (-kt+p)<0 or t < p/k S is maximum when t= p/k the maximum value = A(p/k)pe-p.

1. A drug response curve describes the level of medication in the bloodstream after a drug is
administered. A surge function
Solution
dS/dt = d(Atpe-kt)/dt
= Atp(-k)e-kt+Ae-kt(ptp-1)
= Ae-kttp-1(-kt+p)
Since A, e-kt, tp-1 are positive (t>0)
S is decreasing when dS/dt is negative when (-kt+p)<0 or t > p/k
S is increasing when dS/dt is positive when (-kt+p)<0 or t < p/k
S is maximum when t= p/k
the maximum value = A(p/k)pe-p