Single Variable Calculus, Chapter 3, 3.5, Section 3.5, Problem 78

Suppose that the model for the length of daylight (in hours) in Philadelphia on the tth day of the year us $L(t) = 12 + 2.8 \sin \displaystyle \left[ \frac{d \pi}{365} (t -80) \right]$. Use this model to compare how the number of hours of daylight is increasing in Philadelphia on March 21 and May 21.


$\begin{equation} \begin{aligned} \frac{dL}{dt} =& 2.8 \cos \left[ \frac{2 \pi}{365} (t - 80) \right] \left( \frac{2 \pi}{365} \right) \\ \\ \frac{dL}{dt} =& \frac{5.6 \pi}{365} \cos \left[ \frac{2 \pi}{365} (t - 80) \right] \\ \\ & \text{On March 21, the 80th day of the year,} \\ \\ \frac{dL}{dt} =& \frac{5.6 \pi}{365} \cos \left[ \frac{2 \pi}{365} (80 - 80) \right] \\ \\ \frac{dL}{dt} =& 0.0482 \text{ hours/ day} \\ \\ & \text{On May 21, the 141st day of the year,} \\ \\ \frac{dL}{dt} =& \frac{5.6 \pi}{365} \cos \left[ \frac{2 \pi}{365} (141 - 80) \right] \\ \\ \frac{dL}{dt} =& 0.0240 \text{ hours/day } \end{aligned} \end{equation}$