Chapter 0.1, Problem 60E

Technology Exercises

Response of a Muscle When a solution of acetylcholine is introduced into the heart muscle of a frog, it diminishes the force with which the muscle contracts. The data from experiments of the biologist A. J. Clark are closely approximated by a function of the form

$R\left(x\right)=\frac{100x}{b+x},x\ge 0$,

where $x$ is the concentration of acetylcholine (in appropriate units), $b$ is a positive constant that depends on the particular frog, and $R\left(x\right)$ is the response of the muscle to the acetylcholine, expressed as a percentage of the maximum possible effect of the drug.

Suppose $b=15$. Find the response of the muscle when $x=30$.

Determine the value of $b$ if $R\left(50\right)=30$

; that is, if a concentration of $x=50$ units produces a $30\%$ response.