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.

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

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 the nearest hundredth.

(a) $t=36$ and $t=42$
(b) $t=38$ and $t=42$
(c) $t=40$ and $t=42$
(d) $t=42$ and $t=44$

(What are your conclusions?)

(a)
(b)
(c)
(d)