A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t minutes. When the data in.

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Presentation transcript:

A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t minutes. When the data in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute. The monitor estimates this value by calculating the slope of a secant line. Use the data to estimate the patient's heart rate after 42 minutes using the secant line between the points with t = 38 and t = 42. t (min) 36 38 40 42 44 Heartbeats 2,500 2,700 2,900 2,990 3,050 Choose the correct answer from the following: 145 -71.5 77.5 82.5 71.5 72.5 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

If a ball is thrown into the air with a velocity of 45 ft/s, its height in feet after t seconds is given by {image} . Find the instantaneous velocity when t = 5. -85 -102 -97 -95 -91 -96 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The displacement (in feet) of a certain particle moving in a straight line is given by {image} where t is measured in seconds. Find the average velocity over the interval [1, 1.7]. 1.4075 1.3985 1.2965 1.3975 1.3875 1.5075 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

The point P(1, 0) lies on the curve {image} The point P(1, 0) lies on the curve {image} . If Q is the point ( {image} ), find the slope of the secant line PQ (correct to four decimal places) for {image} . m PQ = 2.1651 m PQ = 2.1653 m PQ = -2.1651 m PQ = -2.1650 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after t minutes. If P is the point (15, 284 ) on the graph of V, find the slope of the secant line PQ when Q is the point on the graph with t = 25. t (min) 5 10 15 20 25 30 V (gal) 652 465 284 174 17 0 Choose the correct answer from the following: -36.8 -26.7 -18.933333 22 18.933333 26.7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50