Chapter 2.3, Problem 44E

Reaction of a Frog to a Drug Experiments conducted by A. J. Clark suggest that the response R(x) of a frog’s heart muscle to the injection of x units of acetylcholine (as a percent of the maximum possible effect of the drug) may be approximated by the rational function

$R\left(x\right)=\begin{array}{c}100x\\ b+x\end{array}$ (x ≥ 0)

where b is a positive constant that depends on the particular frog.

1. a. If a concentration of 40 units of acetylcholine produces a response of 50% for a certain frog, find the “response function” for this frog.
2. b. Using the model found in part (a), find the response of the frog’s heart muscle when 60 units of acetylcholine are administered.