Calc1Problems

# Calc1Problems - 1 Find a formula for the area of a circular ring whose inner radius is r and whose outer radius is r 1(Figure 1 This is a LINEAR

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JL1 8/03 1 1. Find a formula for the area of a circular ring whose inner radius is r and whose outer radius is r + 1 (Figure 1). This is a LINEAR FUNCTION because its graph is a straight line. Sketch its graph in an rA -plane Figure 1 2. (a) Give approximate values of A (1) and A (4) for the function A ( x ) of Figure 2. (b) Find the approximate solutions x of A ( x ) = 40 and of A ( x ) = 60 with 0 x 6. (c) Which is greater [ A (2)] 2 or A (2 2 )? Explain. Figure 2 3. The symbols A (2) have one meaning if A ( x ) is a function of x and another if A represents a constant. Explain. 4. What are p (1), p (2), and p (3) if the points (1, 18), (2 –6), and (3, ) are on the graph of p ? 5. Figure 3 shows the graph of the velocity v (t) of a woman’s car t seconds after she leaves a parking space. She stops at a traffic light and then goes on the freeway. Give approximate answers to the following questions: (a) How long does she wait at the light? (b) The speed limit is 55 miles per hour, and her trip is interrupted when she is stopped and given a speeding ticket. When do you imagine she sees the highway patrolman who stopped her? (c) During what time interval does she exceed the speed limit on the freeway? (d) During part of the short drive between the parking space and the traffic light, she drives at a constant speed. What is it? How far does she travel during that time? (Remember that an hour consists of 60 x 60 = 3600 seconds.)

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JL1 8/03 2 Figure 3
JL1 8/03 3 6. The next table gives the number of registered political action committees (PAC’s) and the amounts they contributed to candidates for the U. S. Congress during the campaigns for the 1974 through 1988 elections. The contributions have been rounded to the nearest thousand dollars. (a) What were the least and greatest increases in the number of PAC’s from one election to the next during these years? (b) What were the least and greatest increases in the amounts contributed by PAC’s? (c) What was the average amount contributed per PAC in 1974? In 1988? POLITICAL ACTION COMMITTEES, 1974 - 1988 Year 1974 1976 1978 1980 1982 1984 1986 1988 Number of PAC’s 608 1146 1653 2551 3371 4009 4157 4268 Total contributions (million dollars) 12.527 22.572 34.121 55.217 86.620 105.330 132.671 147.898 7. A function Q has the values Q (5) = 7 and Q (10) = 21. What are (a) 10 Q (10), (b) Q (6 + 3 + 1), (c) Q (100/20), (d) Q (10)/ Q (5), and Q ( Q (5) + 3))? 8. The average number of cigarettes C ( t ) smoked per person in the United States is given below for 1945 and every sixth year until 1987. (a) What are the change and relative change of C ( t ) from 1945 to 1963? (b) What are the change and relative change of C ( t ) from 1963 to 1987? (c) C ( t ) has been defined for all t between 1945 and 1987 in Figure 4 by joining the points given in the table with line segments. Find C (1953). This is the average number of cigarettes smoked per capita in 1953 according to the mathematical model in Figure 4. In fact, the average that year was 3500 cigarettes per person. What error is made by using C (1953)? What is the relative error (the error divided by the correct value)? (d) In Figure 4 the numbers on the vertical axis run from 3000 to 4500. Figure 5 shows the same graph with all of the vertical axis shown from 0 to 4500. Both graphs give good representations of changes in C ( t

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## This note was uploaded on 10/18/2011 for the course MAC 2311 taught by Professor Jameslang during the Fall '11 term at Valencia.

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Calc1Problems - 1 Find a formula for the area of a circular ring whose inner radius is r and whose outer radius is r 1(Figure 1 This is a LINEAR

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