# Rational Functions Word Problem

• Sep 10th 2012, 07:38 PM
AntoninaFinn
Rational Functions Word Problem
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 appromixated by the rational function
R(x)=100x/b+x (x greater than or equal to 0)
where b is a positive constant that depends on the particular frog.
a. If concentration of 40 units of acetylcholine produces a response of 50% for a certain frog, find the "response function" for this frog.
b. Using the model found in part (a), find the response of the frog's heart when 60 units of acetylcholine are administered.

I am so confused by this problem.

Help would be greatly appreciated.
• Sep 10th 2012, 09:55 PM
kalyanram
Re: Rational Functions Word Problem
Given $R(x)=\frac{100x}{b+x}$; where $R(x)$ is the response function (measure in percentage); $x$ (in concentration)
a. Given $R(40)=50$ we need to now determine $b$ which is specific to the frog under test.
$50=\frac{100.40}{b+40} \implies b=40; \therefore R(x)=\frac{100x}{40+x}$
Now you can try part (b).