$\"\"$

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

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The number of patients heartbeats are taken in the table for different values of time $\"\"$ .

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Find the slope of the secant lines between the points using the table of values.

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(a)

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Find the slope at $\"\"$ and $\"\"$ .

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At $\"\"$ and the corresponding patient heartbeat is $\"\"$ .

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At $\"\"$ and the corresponding the patient heartbeat is $\"\"$ .

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So the obtained points are $\"\"$ and $\"\"$ .

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Slope of the two points is $\"\"$ .

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The slope of the secant line is $\"\"$ heartbeats/min.

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$\"\"$

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(b)

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Find the slope at $\"\"$ and $\"\"$ .

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At $\"\"$ and the corresponding patient heartbeat is $\"\"$ .

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At $\"\"$ and the corresponding the patient heartbeat is $\"\"$ .

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So the obtained points are $\"\"$ and $\"\"$ .

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Slope of the two points is $\"\"$ .

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The slope of the secant line is $\"\"$ heartbeats/min.

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$\"\"$

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(c)

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Find the slope at $\"\"$ and $\"\"$ .

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At $\"\"$ and the corresponding patient heartbeat is $\"\"$ .

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At $\"\"$ and the corresponding the patient heartbeat is $\"\"$ .

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So the obtained points are $\"\"$ and $\"\"$ .

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Slope of the two points is $\"\"$ .

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The slope of the secant line is $\"\"$ heartbeats/min.

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$\"\"$

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(d)

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Find the slope at $\"\"$ and $\"\"$ .

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At $\"\"$ and the corresponding patient heartbeat is $\"\"$ .

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At $\"\"$ and the corresponding the patient heartbeat is $\"\"$ .

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So the obtained points are $\"\"$ and $\"\"$ .

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Slope of the two points is $\"\"$ .

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The slope of the secant line is $\"\"$ heartbeats/min.

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Conclusion :

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After $\"\"$ minutes the patients heart rate decreases.

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$\"\"$

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Find the patient heart rate after $\"\"$ minutes.

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Use the average of the slopes of the patients heart rate after $\"\"$ minutes.

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So consider the points near to $\"\"$ are $\"\"$ and $\"\"$ .

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The slope of the heart rate at $\"\"$ and $\"\"$ is $\"\"$ heartbeats/min.

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The slope of the heart rate at $\"\"$ and $\"\"$ is $\"\"$ heartbeats/min.

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The average of the slopes is $\"\"$ heartbeats/min.

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The patient heart rate after $\"\"$ minutes is $\"\"$ heartbeats/min.

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$\"\"$

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(a) $\"\"$ heartbeats/min.

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(b) $\"\"$ heartbeats/min.

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(c) $\"\"$ heartbeats/min.

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(d) $\"\"$ heartbeats/min.

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The patient heart rate after $\"\"$ minutes is $\"\"$ heartbeats/min.