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2. A cardiac monitor is used to measure the heart rate of a patient after surger

ID: 2890041 • Letter: 2

Question

2. A cardiac monitor is used to measure the heart rate of a patient after surgery. It compiles the number of heartbeats after t min utes. When the data in the table are graphed, the slope of the tangent line represents the heart rate in beats per minute. t (min) 36 38 40 42 44 Heartbeats 2530 2661 2806 2948 3080 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 the given values of t. (a) t=36 and t=42 (c) t= 40 and t=42 (b) t=38 and t=42 (d) t=42 and t=44 What are your conclusions?

Explanation / Answer

Solution:

The slope of a straight line on the graph joining two points at times t1 and t2 with corresponding heartbeat rates h1 and h2 is:    = (h2 - h1) / (t2 - t1)

(a) t = 36 and t = 42

m = (2948 - 2530) / (42 - 36) = 418 / 6 = 69.67

(b) t = 38 and t = 42

m = (2948 - 2661) / (42 - 38) = 287 / 4 = 71.75

(c) t = 40 and t = 42

m = (2948 - 2806) / (42 - 40) = 142 / 2 = 71

(d) t = 42 and t = 44

m = (3080 - 2948) / (44 - 42) = 132 / 2 = 66