176 CHAPTER 3 Linear and Quadratic Functions ‘Are You Prepared?’ Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 3.4 Assess Your Understanding 1. Translate the following sentence into a mathematical equation: The area A of a circle equals the product of the square of its radius r and the constant .π (p. A67 ) 2. Use a graphing utility to find the line of best fit for the following data: (pp. 149–153) x 3 5 5 6 7 8 y 10 13 12 15 16 19 3. Maximizing Revenue The price p (in dollars) and the quantity x sold of a certain product satisfy the demand equation x p6 600 = − + (a) Find a model that expresses the revenue R as a function of p. (Remember, R xp. = ) (b) What is the domain of R? Assume R is nonnegative. (c) What price p maximizes the revenue? (d) What is the maximum revenue? (e) How many units are sold at this price? (f) Graph R. (g) What price should the company charge to earn at least $12,600 in revenue? 4. Maximizing Revenue The price p (in dollars) and the quantity x sold of a certain product satisfy the demand equation x p3 360 = − + (a) Find a model that expresses the revenue R as a function of p. (b) What is the domain of R? Assume R is nonnegative. (c) What price p maximizes the revenue? (d) What is the maximum revenue? (e) How many units are sold at this price? (f) Graph R. (g) What price should the company charge to earn at least $9600 in revenue? 5. Maximizing Revenue The price p (in dollars) and the quantity x sold of a certain product satisfy the demand equation x p5 100 = − + (a) Find a model that expresses the revenue R as a function of p. (b) What is the domain of R? Assume R is nonnegative. (c) What price p maximizes the revenue? (d) What is the maximum revenue? (e) How many units are sold at this price? (f) Graph R. (g) What price should the company charge to earn at least $480 in revenue? 6. Maximizing Revenue The price p (in dollars) and the quantity x sold of a certain product satisfy the demand equation x p 20 500 = − + (a) Find a model that expresses the revenue R as a function of p. (b) What is the domain of R? Assume R is nonnegative. (c) What price p maximizes the revenue? (d) What is the maximum revenue? (e) How many units are sold at this price? (f) Graph R. (g) What price should the company charge to earn at least $3000 in revenue? 7. Enclosing a Rectangular Field David has 400 yards of fencing and wishes to enclose a rectangular area. (a) Express the area A of the rectangle as a function of the width w of the rectangle. (b) For what value of w is the area largest? (c) What is the maximum area? 8. Enclosing a Rectangular Field Beth has 3000 feet of fencing available to enclose a rectangular field. (a) Express the area A of the rectangle as a function of x, where x is the length of the rectangle. (b) For what value of x is the area largest? (c) What is the maximum area? 9. Enclosing the Most Area with a Fence A farmer with 4000 meters of fencing wants to enclose a rectangular plot that borders on a river. If the farmer does not fence the side along the river, what is the largest area that can be enclosed? (See the figure.) 4000 2 2x x x Applications and Extensions 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
RkJQdWJsaXNoZXIy NjM5ODQ=