6. [-/1 Points] DETAILS LCALCCON5 3.1.501.XP. An artisan makes hand-crafted painted benches to sell at a craft mall. Her weekly revenue and costs (not including labor) are given in the table. Weekly Revenue and Costs for Hand-crafted Benches Number of benches Weekly revenue, R Weekly cost, c sold each week, (dollars) (dollars) 298 6: 3 881 75 5 1366 95 7 1740 128 9 1965 136 11 1940 192 13 1690 219 (@) Find a quadratic model for revenue. (Round all numerical values to three decimal places.) R(n) = dollars Find a cubic model for cost. (Round all numerical values to three decimal places.) C(n) = dollars Using the previous models for revenue and cost, find a cubic model for profit, P. (Round all numerical values to three decimal places.) P(n)= dollars (b) Write the derivative formula for profit. p(n) = per bench (c) Find and interpret the rates of change of profit when the artisan sells 5, 9, and 10 benches, respectively. (Round your answers to two decimal places.) P'(5) = $ per bench When the artisan makes 5 benches, the profit is (.-Select w | by $ per bench. P'(9) = $ per bench When the artisan makes 9 benches, the profit is [- Select- w ) by $ per bench. P ( 10) = $ per bench When the artisan makes 10 benches, the profit is (-Select- w ] by $ per bench. d) Use the information in part (c) to determine the number of benches the artisan should produce each week for maximum profit. benches Need Help? Read Is 7. [-/1 Points] DETAILS LCALCCONS 3.1.036. The table gives the cumulative sales of iPods since their introduction. Cumulative iPod Sales Sales Year (million iPods) 2003 3.22 2004 5.736 2005 29.333 2006 56.642 2007 120.572 2008 173.9 a) Find the function for the quadratic model that gives sales in million iPods, where x is the number of years after 2003, with data from 0 s x 's 5. (Round all numerical values to three decimal places.) S(X) = million ipods (b) Write the derivative for the sales model. (Round all numerical values to three decimal places.) s'(x) = million ipods per year c) Calculate the rate of change of cumulative sales in 2007. (Round your answer to three decimal places.) million ipods per year Interpret the rate of change of cumulative sales in 2007. (Round your answer to three decimal places.) in 2007, cumulative ipod sales were [- Select - v ] by million per year. Need Help? Read :1. [-/1 Points] DETAILS LCALCCON5 3.4.037. The sales of Sherwin-williams paint in different regional markets depends on several input variables. One variable that partially drives selling price, which in turn affects sales, is the cost to get the product to market. When other input variables are held constant, sales can be modeled as s(x) = 597.3(0.9214x + 12) thousand gallons ists x dollars to get a gallon of paint to market, data from 0 S x s 2.+ (a) How many gallons of paint are sold when it costs 15 cents for a gallon to reach the market? (Round your answer to three decimal places.) |thousand gallons (b) How quickly are sales changing when x = 0.15? (Round your answer to three decimal places.) thousand gallons per dollar Need Help? Read Is 2. [-/1 Points] DETAILS LCALCCON5 3.6.023. A store has determined that the number of Blu-ray movies sold monthly is approximately "(x) = 6250(0.926*) movies where x is the average price in dollars. (a) Write the function for the model giving revenue in dollars, where x is the average price in dollars. R(X) = dollars (b) If each movie costs the store $10.00, write the function for the model that gives profit in dollars, where x is the average price in dollars. P(X ) = dollars (c) Complete the table. (Round your answers to three decimal places.) Rates of Change of Revenue and Profil Rate of change career change price (dollars per dollar) (dollars per dollar) $13 $14 $20 $21 $22 (d) What does the table indicate about the rate of change in revenue and the rate of change in profit at the same price? There is a range of prices beginning near $14 for which the rate of change of revenue is (Select- * ) (revenue is (-Select.. . ) ) while the rate of change of profit is Select- w ) (profit is Select ) ) Need Help? Read ! 3. [-/1 Points] DETAILS LCALCCON5 3.6.501.XP. The accompanying table gives the number of men 65 years or older in the United States and the percentage of men age 65 or older living below the poverty level. Year Men 65 years or older, m (millions) Percentage below poverty level, p 1970 B.3 20.2 1980 10.3 11.1 1985 11.0 8.7 1990 12.6 7.8 1997 14.0 7.0 2000 14.4 7.5 (a) Using time as the input, find a linear model for the data set for the number men 65 years or older in the United States. (Let x be the years since 1970. Round all numerical values to three decimal places.) m(x) = million men Using time as the input, find a quadratic model for the data set for the percentage of men age 65 or older below poverty level. (Let x be the years since 1970. Round all numerical values to three decimal places.) P(X) = (b) Write an expression for the number of men 65 years or older who are living below the poverty level in the United States. n(x)= million men (c) How rapidly was the number of male senior citizens living below the poverty level changing in 1975 and in 19857 (Round your answer to three decimal places.) 1975 million men per year 1985 million men per year Need Help? Read Is