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

Question

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 the given values of t. (Round your answers to one decimal place.)

(a)    t = 36 and t = 42


(b)    t = 38 and t = 42


(c)    t = 40 and t = 42


(d)    t = 42 and t = 44

Explanation / Answer

a)68.833
b)67.75
c)67
d)67

For your problem:

Pt -t(min) - heartbeats
1 -- 36 --- 2530
2 -- 38 --- 2672
3 -- 40 --- 2809
4 -- 42 --- 2943
5 -- 44 --- 3077

Slope = y/x
Let x = time, y = heartbeats

Slope(1~4) = (2943-2530) / (42-36)
Slope(1~4) = 413/6 = 68.833

Slope(2~4) = (2943-2672) / (42-38)
Slope(2~4) = 271/4 = 67.75

Slope(3~4) = (2943-2809) / (42-40)
Slope(3~4) = 134/2 = 67

Slope(4~5) = (3077 - 2943) / (44-42)
Slope(4~5) = 134/2 = 67

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