Sales volume Suppose that the weekly sales volume (in thousands of units) for a product is given by
(a) for all values of
(c) for all
(d) What is the domain for this application?
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Chapter 9 Solutions
Mathematical Applications for the Management, Life, and Social Sciences
- Decomposing Functions If f(x)=x2+3, express f as a composition of two functions.arrow_forwardMaximum Sales Growth This is a continuation of Exercise 10. In this exercise, we determine how the sales level that gives the maximum growth rate is related to the limit on sales. Assume, as above, that the constant of proportionality is 0.3, but now suppose that sales grow to a level of 4 thousand dollars in the limit. a. Write an equation that shows the proportionality relation for G. b. On the basis of the equation from part a, make a graph of G as a function of s. c. At what sales level is the growth rate as large as possible? d. Replace the limit of 4 thousand dollars with another number, and find at what sales level the growth rate is as large as possible. What is the relationship between the limit and the sales level that gives the largest growth rate? Does this relationship change if the proportionality constant is changed? e. Use your answers in part d to explain how to determine the limit if we are given sales data showing the sales up to a point where the growth rate begins to decrease.arrow_forwardSales Growth In this exercise, we develop a model for the growth rate G, in thousands of dollars per year, in sales of the 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 difference this limit and the current sales level. For example, if we expect sales grow to 3 thousand dollars in the long run, then 3-s is 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 0.3 and that the sales grow to 2 thousand dollars in the long run. a.Find the formula for unattained sales. b.Write an equation that shows the proportionality relation for G. c.On the basis of the equation from the part b, make a graph of G as a function of s. d.At what sales level is the growth rate as large as possible? e.What is the largest possible growth rate?arrow_forward
- Changing Water Levels The graph shows the depth of water W in a reservoir over a one-year period as a function of the number of days x since the beginning of the year. What was the average rate of change of W between x=100 and x=200?arrow_forwardAdding Functions A certain function f is the sum of two temperatures, one given by t2+3, and the other given by tt2+1. Find a formula for f in terms of t.arrow_forwardA triangle is formed by the coordinate axes and a line through the point (2,1), as shown in the figure. The value of y is given by y=1+2x2 Write the area A of the triangle as a function of x. Determine the domain of the function in the context of the problem. Sketch the graph of the area function. Estimate the minimum area of the triangle from the graph.arrow_forward
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