Chapter 1, Problem 9PE

Total marketing effort is a term used to describe the critical decision factors that affect demand: price, advertising, distribution, and product quality. Let the variable $x$ represent total marketing effort. A typical model that is used to predict demand as a function of total marketing effort is $D=a{x}^b$ Suppose that $a$ is a positive number. Different models result from varying the constant $b$. Sketch the graphs of these models for $b=0,b=1,0<b<1,b<0,\text{ and }b>1.$ What does each model tell you about the relationship between demand and marketing effort? What assumptions are implied? Are they reasonable? How would you go about selecting the appropriate model?