Thread: Math Word Problem: Rational Functions

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.

I am so confused by this problem. For my answer I have 98.77.

Help would be greatly appreciated.

Originally Posted by AntoninaFinn

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. I am so confused by this problem. For my answer I have 98.77.

b = 400.

I don't think that's right. Aren't they asking for a function?
And what is with all of those x's?
It said to find the "response function". But thanks anyway.

Originally Posted by AntoninaFinn

I don't think that's right. Aren't they asking for a function?
And what is with all of those x's?
It said to find the "response function". But thanks anyway.

R(x)=100x/b+x where b=400

Sorry, Max but that still isn't helping me.
How did you get the 400?

How does the 50% play into the whole function? They said to find the response function, so are you saying that the response function is R(x)=100x/b+x ?
And for the 40 units of acetylcholine, do I substitute into the function that they give me, such as R(40)=100(40)/b+40.

Since part (b) of the problem says that I have to use the model that I found in part (a) to find the response of the frog's heart muscle when 60 units of acetylcholine are administered.

Yes, just calculate R(60)=?%

?