1.

25. 1= + 8x1. +If /x) =\f15. Business The profit In dollars from the sale of x expensive watches Is Paj = 03r - 4r + 3 - 5010. Find the marginal profit for the given values of t. (a) x = 100 (b) x = 1000 (c) x = 5010 (d) x = 10.00017. Business Often, sales of a new product grow rapidly at first and then slow down with time. This is the case with the sales represented by the function Sin = 10.000 - 10,000r ~ + 100r where / represents time in years. Find the rate of change of sales for the given values of r. (b) = 1019. Business The revenue equation (in hundreds of millions of dollars) for barley production in the United States is approxi- mated by R(x) = 0608- + 1.4284: + 2.3418. where x is in hundreds of millions of bushels. (Data from: www. usda.gov.] (a) Find the marginal-revenue function. (b) Find the marginal revenue for the production of 500.000.000 bushels. (c) Find the marginal revenue for the production of 700.000.000 bushels.51. Business The revenue generated from the sale of a picnic tables is given by 500 (a) Find the marginal revenue when & = 1000 units. (b) Determine the actual revenue from the sale of the 1001st Item. (c) Compare the answers to parts (a) and (b). How are they related?57. Business Assume that a demand equation is given by x = 5000 - 100p. Find the marginal revenue for the given production levels (values of x). (Hint: Solve the demand equa- tion for p and use R(x) = xp.) (a) 1000 units (b) 2500 units (c) 3000 units61. Business A marketing firm is interested in the percentage of the total United States population that is age 0-17 years. This percentage can be estimated by Pu) = 2676 . where : = 0 corresponds to the year 2000 and the estimate is valid through the year 2025. Find and interpret the given quantities. (Data from: www.childstats.gov.) (a) P(1 4) and P(14) (b) P(24) and P'(24)63. Social Science The women 's 100-meter dash was intro- dueed to the Olympic Games in 1928. Between 1928 and 2012, the winning time (In seconds) can be approximated by W(x) = .000178- - .0404x + 13.068, where a = 0 corre- sponds to the year 1900. (Data from: www.Olympic.org.) (a) Would you expect the derivative of W(x) to be positive, negative, or zero! Why? (b) Find and interpret the rate of change of W(x) in 1928. (c) Find and interpret the rate of change of Wa) in 2012