In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of a product as a function of the sales level s, in thousands of dollars.† The model assumes that there is a limit to the total amount of sales that can be attained. In this situation, we use the term unattained sales for the difference between this limit and the current sales level. For example, if we expect sales to grow to 4 thousand dollars in the long run, then 4 − s gives the unattained sales. The model states that the growth rate G is proportional to the product of the sales level s and the unattained sales. Assume that the constant of proportionality is 0.8 and that the sales grow to 2 thousand dollars in the long run. (a) Find a formula for unattained sales. (b) Write an equation that shows the proportionality relation for G. G =
In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of a product as a function of the sales level s, in thousands of dollars.† The model assumes that there is a limit to the total amount of sales that can be attained. In this situation, we use the term unattained sales for the difference between this limit and the current sales level. For example, if we expect sales to grow to 4 thousand dollars in the long run, then 4 − s gives the unattained sales. The model states that the growth rate G is proportional to the product of the sales level s and the unattained sales. Assume that the constant of proportionality is 0.8 and that the sales grow to 2 thousand dollars in the long run.
(b) Write an equation that shows the proportionality relation for G.
G =
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