Single Variable Calculus, Chapter 2, 2.1, Section 2.1, Problem 2

The purpose of a cardiac monitor is 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.



$
\begin{equation}
\begin{aligned}

\begin{array}{|c|c|c|c|c|c|}
\hline\\
t(\text{ min }) & 36 & 38 & 40 & 42 & 44 \\
\hline\\
\text{ Heartbeats} & 2530 & 2661 & 2806 & 2948 & 3080\\
\hline
\end{array}

\end{aligned}
\end{equation}
$


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 $t$. State your conclusions.

(a). @ $t=36$ and $t=42$

slope = $\displaystyle \frac{2948-2530}{42-36} = 69.67$


(b). @ $t=38$ and $t=42$

slope = $\displaystyle \frac{2948-2661}{42-38} = 71.75$

(c). @ $t=40$ and $t=42$

slope = $\displaystyle \frac{2948-2806}{42-40} = 71$

(d). @ $t=42$ and $t=44$

slope = $\displaystyle \frac{3080-2948}{44-42} = 66$

Based from the values we obtain, we can conclude that the patient's heart rate is not changing at a constant rate.