Below Are the Sunrise and Sunset Times (In Standard Time) $\text { Sunrise and Sunset in Moorhead, Minnesota on the 21st of each month in } 2007$

Below are the sunrise and sunset times (in standard time) for Moorhead, Minnesota on the 21st of each month in 2007.
$\text { Sunrise and Sunset in Moorhead, Minnesota on the 21st of each month in } 2007$
$\begin{array} { | l | c | c | c | c | } \hline { \text { Date } } & \text { Day of Year } & \text { Sunrise } & \text { Sunset } & \text { Day Length (h) } \\\hline \text { Jan 21 } & 21 & 08 : 03 & 17 : 14 & 9.18 \\\hline \text { Feb 21 } & 52 & 07 : 21 & 18 : 01 & 10.67 \\\hline \text { Mar 21 } & 80 & 06 : 28 & 18 : 41 & 12.22 \\\hline \text { Apr 21 } & 111 & 05 : 29 & 19 : 24 & 13.92 \\\hline \text { May 21 } & 141 & 04 : 45 & 20 : 02 & 15.28 \\\hline \text { Jun 21 } & 172 & 04 : 32 & 20 : 25 & 15.88 \\\hline \text { Jul 21 } & 202 & 04 : 54 & 20 : 12 & 15.30 \\\hline \text { Aug 21 } & 233 & 05 : 32 & 19 : 27 & 13.92 \\\hline\end{array}$
(a) Find the rate of change in day length with respect to time (in hours per day)
(i)
from March 21 through July 21.(ii)
from March 21 through May 21.(iii)
from March 21 through April 21.(b) Estimate the instantaneous rate of change in day length per day (in hours per day) for March 21.(c) During which one-month period did the day length change the greatest amount?
(d) During which one month period did the average change in day length change the greatest amount? Is this the same time period as in part (c)? Explain.