Calculus: An Integrated Approach to Functions and their Rates of Change, Preliminary Edition Part 36. 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 | Exploratory Problems for Chapter 9 331 a If the population has been increasing linearly was the population in 1980 equal to 150 000 greater than 150 000 or less than 150 000 Explain your reasoning. b If the population has been increasing exponentially was the population in 1980 equal to 150 000 greater than 150 000 or less than 150 000 Explain your reasoning. Note Your answers to parts a and b should be different 5. Let D t H t and J t represent the annual salaries in dollars of David Henry and Jennifer and suppose that these functions are given by the following formulas where t is in years. t 0 corresponds to this year s salary t 1 to the salary one year from now and so on. The domain of each function is t 0 1 2 . up to retirement. D t 40 000 2500t H t 50 000 J t 40 000 a Describe in words how each employee s salary is changing. b Suppose you are just four years away from retirement you ll collect a salary for four years including the present year. Which person s situation would you prefer to be your own c If you are in your early twenties and looking forward to a long future with the company which would you prefer 6. In Anton Chekov s play Three Sisters Lieutenant-Colonel Vershinin says the following in reply to Masha s complaint that much of her knowledge is unnecessary. I don t think there can be a town so dull and dismal that intelligent and educated people are unnecessary in it. Let us suppose that of the hundred thousand people living in this town which is of course uncultured and behind the times there are only three of your sort. . Life will get the better of you but you will not disappear without a trace. After you there may appear perhaps six like you then twelve and so on until such as you form a majority. In two or three hundred years life on earth will be unimaginably beautiful marvelous. Man needs such a life and though he hasn t it yet he must have a presentiment of it expect it dream it prepare for it for that he must know more than his .
