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.

Re: Math Word Problem: Rational Functions

Quote:

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**.

Re: Math Word Problem: Rational Functions

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.

Re: Math Word Problem: Rational Functions

Quote:

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**

Re: Math Word Problem: Rational Functions

Sorry, Max but that still isn't helping me.

How did you get the 400?

Re: Math Word Problem: Rational Functions

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.

Re: Math Word Problem: Rational Functions

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.

Re: Math Word Problem: Rational Functions

Yes, just calculate R(60)=?%

Re: Math Word Problem: Rational Functions