Answer
(a) $71$ beats per minute.
$66$ beats per minute.
(b) $68.5$ beats per minute,
Work Step by Step
(a) Based on the table given in the Exercise, the average heart rate or slope of the secant line over the time interval $[40, 42]$ is given by $R_1=\frac{2948-2806}{42-40}=71$ beats per minute.
Similarly, the average heart rate or slope of the secant line over the time interval $[42, 44]$ is given by $R_2=\frac{3080-2948}{44-42}=66$ beats per minute.
(b) The average of the slopes of these two secant lines is given by $R_a=\frac{R_1+R_2}{2}=\frac{71+66}{2}=68.5$ beats per minute, which gives an estimate for the patient’s heart rate after 42 min.
