1. Rewrite the following statements in such a way that they address how rapidly the quantity changed over the given time interval:  John ran 3 miles during the last 30 minutes.  Gas prices have risen $1.30 over the past 6 months.  A waitress served 50 tables in her 6 hour shift. 2. The following table shows the number of raffle tickets a high school football team sold based on different ticket prices. Ticket Price ($) 10 20 30 40 50 # Tickets 1000 600 400 224 100 Use the data to find the average rate at which the profit changes when the ticket price changes from $20 to $40. Answer in a sentence. 3. The graph shows the number of McDonald’s employees in thousands from 1987 through 1996. 
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Approximately how rapidly was the number of employees changing between 1987 and 1989? Draw the straight line through the points corresponding to the years 1987 and 1989. How is this rate of growth of the number of employees related to the slope of that line? Explain in a sentence or two. 4. The population of Indiana by official census from 1900 through 1990 can be modeled using the equation P(t) = "0.129t 2 + 2.2t " 3.88 , where t is the number of decades since 1900.  How much did the population change from 1920 to 1950?  How rapidly did the population change from 1920 to 1950?  Is t!
he phrase “on average” necessary here? Why or why not? 5. The annual amount of dividends paid to stockholders of the Houghton Mifflin Company for the years 1990 to 1994 are shown in the table below. The graph of a cubic model to imitate this data is shown as well. We want to estimate how fast the annual amount of dividends paid was growing/declining at the point marked as 1995 on the horizontal axis. 
Use the tangent line method to estimate how fast the annual amount of dividends paid to stockholders was growing at the point marked 1995. Report your findings in a sentence. 6. At each labeled point, decide if the quantity y is changing at a positive, negative or zero rate? Is the graph steeper at point A or point C? 7. The table below gives the price, in dollars, of a round-­‐trip flight from Denver to Chicago on a certain airline and the corresponding monthly profit for that airline on that route. Ticket Price ($)
Profit (thousands $)
200
3080
250
3520
300
3760
350
3820
400
3700
450
3380
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Find a model for the data. Graph the model below. Use the tangent line method to estimate the rate at which the profit is changing when the ticket price is $300.  Now, using your equation, use the numerical method to estimate how rapidly the profit is changing when the ticket price is $300. Estimate the rate repeatedly, until you are quite certain that you have the rate correct to 2 decimal places. Beginning at p = $300 Ending at p = $300 With p = 300 in the middle 
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At what rate is the profit changing when the ticket price is $300? Answer in a complete sentence. Compare your answers using the tangent line method and numerical method. Are they the same? Why or why not? Explain in a sentence or two. 8. The function w gives the number of words per minute that a student in a keyboarding class can type after t weeks in the course.  Is it possible for w(t) to be negative? Explain.  What are the units of w’(t)?  Is it possible for w’(t) to be negative? Explain. 9. The function t gives the number of one-­‐way tickets from Boston to Washington D.C. that a certain airline sells in one week when the price of each ticket is p dollars. Interpret the following:  t(115) = 1750  t’(65) = 1.5  t’(90) = -­‐2 10. The function E gives the public secondary school enrollment, in millions of students, in the United States between 1940 and 2008. The input t represents the number of years since 1940. Use the following information to sketch a graph of E.  E(40) = 13.2  The graph of E is always concave down.  Between 1980 and 1990, enrollment declined at an average rate of 0.19 million students per year.  The projected enrollment for 2008 is 14,400,000.