Supply In Exercises 53 and 54, find the supply function
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Calculus: An Applied Approach (MindTap Course List)
- Milk Production Milk production M (in billions of pounds) in the United States from 2000 through 2014 can be modeled by M=3.00t+163.3,0t14 where t represents the year, with t = 0 corresponding to 2000. (a) According to the model, when was the annual milk production greater than 180 billion pounds, but no more than 190 billion pounds? (b) Use the model to predict when milk production will exceed 230 billion pounds.arrow_forwardProjectile Motion In Exercises 75 and 76, consider the path of an object projected horizontally with a velocity of v feet per second at a height of s feet, where the model for the path is x2=v216ys. In this model (in which air resistance is disregarded), y is the height (in feet) of the projectile and x is the horizontal distance (in feet) the projectile travels. A ball is thrown from the top of a 100-foot tower with a velocity of 28 feet per second. (a) Write an equation for the parabolic path. (b) How far does the ball travel horizontally before it strikes the ground?arrow_forwardSelling concert tickets Tickets for a concert are cheaper when purchased in quantity. The first 100 tickets are priced at 10 each, but each additional block of 100 tickets purchased decreases the cost of each ticket by 50. How many blocks of tickets should be sold to maximize the revenue?arrow_forward
- Drug Concentration When a drug is administered orally, it takes some time before the blood concentration reaches its maximum level. After that time, concentration levels decrease. When 500 milligrams of procainamide is administered orally, one model for a particular patient gives blood concentration C, in milligrams per liter, after t hours as C=2.65(e0.2te2t) What is the maximum blood-level concentration, and when does that level occur?arrow_forwardVoting-Age Population The total voting-age population P (in millions) in the United States from 1990 through 2014 can be modeled by P=184.64+0.7524t21+0.0028t2,0t24 where t represents the year, with t=0 corresponding to 1990. (a) In which year did the total voting-age population reach 210 million? (b) Use the model to predict when the total voting-age population will reach 260 million. Is this prediction reasonable? Explain.arrow_forwardPopulation Statistics The table shows the life expectancies of a child (at birth) in the United States for selected years from 1940 through 2010. A model for the life expectancy during this period is y=63.6+0.97t1+0.01t,0r70 Where y represents the life expectancy and t is the time in years, with t=0 corresponding to 1940. (a) Use a graphing utility to graph the data from the table and the model in the same viewing window. How well does the model fit the data? Explain (b) Determine the life expectancy in 1990 both graphically and algebraically. (c) Use the graph to determine the year when life expectancy was approximately 70.1. Verify your answer algebraically. (d) Identify the y-intercept of the graph of the model. What does it represent in the context of the problem? (e) Do you think this model can be used to predict the life expectancy of a child 50 years from now? Explainarrow_forward
- Analysis of daily output of a factory during a 8-hour shift shows that the hourly number of units y produced after t hours of production is y = 10t + 1 2 t2 − t3, 0 ≤ t ≤ 8. (a) After how many hours will the hourly number of units be maximized? hr (b) What is the maximum hourly output? units/hrarrow_forwardSuper Bowl Ads A minute ad during Super BowlVII in 1973 cost $200,000. The price tag for a30-second ad slot during the 2011 Super Bowlwas $3 million. The cost of a 30-second slot ofadvertising for the Super Bowl can be modeled byy = 0.0000966(1.101x ), where x is the number ofyears after 1900 and y is the cost in millions.a. According to the model, what was the cost of a30-second Super Bowl ad in 2000?b. The cost of a 30-second ad during Super Bowl XLIXin 2015 was $4.5 million. Does the model underestimate or overestimate the cost of these ads?arrow_forwardEquilibrium Price: Skateboards The demand for your hand-made skateboards, in weekly sales, is q = −6p + 700 if the selling price is $p. You are prepared to supply q = 4p − 400 per week at the price $p. What price should you sell your skateboards for so that there is neither a shortage nor a surplus? $ per skateboardarrow_forward
- Analysis of daily output of a factory during a 8-hour shift shows that the hourly number of units y produced after t hours of production is y = 102t + 1 2 t2 − t3, 0 ≤ t ≤ 8. (a) After how many hours will the hourly number of units be maximized? hr(b) What is the maximum hourly output? units/hrarrow_forwardThe reproduction function for a sardine is f(p) = −0.0004p2 + 2p, where p and f(p) are in hundred metric tons. Find the population that gives the maximum sustainable yield, and the size of the yield. population = Size of the yield=arrow_forward
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