The concentration (in mg/L) of an intravenous drug in a patient’s bloodstream is…

MATHEMATICS · Multi-part · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

The concentration

C

(in mg/L) of an intravenous drug in a patient’s bloodstream is modeled for

t>B

minutes after administration by

C(t)=\frac{A}{t-B}+C_0,

where

A>0

B>0

, and

C_0>0

are constants determined empirically. (a) Find the vertical asymptote of

C

and interpret its clinical significance. (b) A safety protocol declares concentrations above a threshold

S

mg/L to be hazardous. Solve the inequality

C(t)>S

for

t>B

in terms of

A

B

C_0

, and

S

. (c) For fixed

A

and

C_0

, derive an expression that gives the elapsed time between

t=B

and the first moment the concentration falls below the safety threshold

S

. Comment on how changing

B

affects this duration.