Supply In Exercises 53 and 54, find the supply function
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Chapter 5 Solutions
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_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.arrow_forward
- The national defense budget expenses V (in billions of dollars) for veterans in the United States from 1990 to 2005 can be approximated by the model *Picture of model included* where t represents the year, with t = 0 corresponding to 1990. Use the model to find total veteran expenses in 1999.arrow_forwardAnalysis 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_forwardReading Score The average reading score on theNational Assessment of Progress tests is given byy = 0.155x + 255.37, where x is the number ofyears after 1970. In what year would the averagereading score be 259.4 if this model is accurate?arrow_forward
- The 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_forwardA container can contain 240 Gallon of clear water. The clear water containing 4 lbs of sugar per Gal enters the Container at a rate of 16 Gal/Minute, and the A fully mixed solution is pumped out of the container at a constant rate of 8 Gal/Min. Originally, the container contains clear water and has a max. capacity of 500 Gal. Find the t-interval of interest and how much sugar is in the container after 25 minutes.arrow_forwardCalculus A 900 L tank contains 450 L of water with a salt concentration of 14 g/L. Water with a salt concentration of 47 g/L flows into the tank at a rate of 82 L/min. The fluid mixes instantaneously, and is pumped out at a specified rate 44 L/min. Let y(t) denote the quantity of salt in the tank at time t. What is the salt concentration when the tank overflows?arrow_forward
- A swimming pool holds 12,500 gallons of water at the start of the day. A valve at the bottom of the pool releases water into a cleaning tank at a constant rate of 20 gallons per hour. A hose is running water into the pool at a constant rate of 60 gallons per hour. On one day, the hose was running for 3 hours, and the valve was left open for 6 hours. How much water is in the pool at the end of the day?arrow_forwardDemand Function Supply Function p = 133 − 0.5x p = 0.002x2 + 13 Find the consumer and producer surpluses (in dollars) by using the demand and supply functions, where p is the price (in dollars) and x is the number of units (in millions).arrow_forwardAnalysis 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_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning