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Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 27. A major complaint of professors teaching calculus is that students don't have the appropriate background to work through the calculus course successfully. This text is targeted directly at this underprepared audience. This is a single-variable (2-semester) calculus text that incorporates a conceptual re-introduction to key precalculus ideas throughout the exposition as appropriate. This is the ideal resource for those schools dealing with poorly prepared students or for schools introducing a slower paced, integrated precalculus/calculus course | 6.4 The Free Fall of an Apple A Quadratic Model 241 PROBLEMS FOR SECTION 6.4 1. A seat on a round-trip charter flight to Cairo costs 720 plus a surcharge of 10 for every unsold seat on the airplane. If there are 10 seats left unsold the airline will charge each passenger 720 100 820 for the flight. The plane seats 220 travelers and only round-trip tickets are sold on the charter flights. a Let x the number of unsold seats on the flight. Express the revenue received for this charter flight as a function of the number of unsold seats. Hint Revenue price surcharge number of people flying . b Graph the revenue function. What practically speaking is the domain of the function c Determine the number of unsold seats that will result in the maximum revenue for the flight. What is the maximum revenue for the flight 2. Troy is interested in skunks and has purchased a bevy of them to study. He plans to keep the skunks in a rectangular skunk corral as shown below. He will have a divider across the width in order to separate the males and females. He has 510 meters of fencing to make his corral. a Let x the width of the corral and y the length of the corral. Use the fact that Troy has only 510 meters of fencing to express y in terms of x. b Express A the total area enclosed for the skunks as a function of x. c Find the dimensions of the corral that maximize the total area inside the corral. divider 3. The height of a ball in feet t seconds after it is thrown is given by h t -16t2 32t 48 16 t 1 t - 3 . a Graph h t for the values of t for which it makes sense. Below it graph v t . Be sure that v t looks like the derivative of h t . b From what height was the ball thrown c What was the ball s initial velocity Was it thrown up or down How can you tell d Was the ball s height increasing or decreasing at time t 2 e At what time did the ball reach its maximum height How high was it then What was its velocity at that time f How long was the ball in the air g What is the ball s .
