Help with a 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.
I've had to post this more than I had wanted to, simply because I haven't been able to receive a thorough answer with steps attached and the why.
Re: Help with a functions word problem
I assume you meant to write R(x)=100x/(b+x).
a) This translates to "When x = 40, R = .5. Find R(x)". Which means "Use R(40)=.5 to find b, and then write down the formula for R(x) with that b."
b) This translates to "Using the R(x) found in part (a), find R(60).".
Part (a) amounts to solving an equation for b ("Use R(40)=.5 to find b"), and Part b is just plugging x=60 and the discovered value for b into the formula.
I hope that helps clarify how you should proceed.