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

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

(a) Suppose b = 15. Find the response of the muscle when x = 30.

(b) Determine the value of b if R(50) = 30; that is, if a concentration of x = 50 units produces a 30% response.

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R(x) = 100x b + x² x ≥ 0,