Hours of daylight The number of hours of daylight at any pointon Earth fluctuates throughout the year. In the Northern Hemisphere, the shortest day is on the winter solstice and the longestday is on the summer solstice. At 40° north latitude, the length ofa day is approximated by where D is measured in hours and 0 < t < 365 is measured indays, with t = 0 corresponding to January 1.a. Approximately how much daylight is there on March 1(t = 59)?b. Find the rate at which the daylight function changes.c. Find the rate at which the daylight function changes on March 1.Convert your answer to units of min/day and explain whatthis result means.d. Graph the function y = D′(t) using a graphing utility.e. At what times of the year is the length of day changing mostrapidly? Least rapidly?
Hours of daylight The number of hours of daylight at any point
on Earth fluctuates throughout the year. In the Northern Hemisphere, the shortest day is on the winter solstice and the longest
day is on the summer solstice. At 40° north latitude, the length of
a day is approximated by where D is measured in hours and 0 < t < 365 is measured in
days, with t = 0 corresponding to January 1.
a. Approximately how much daylight is there on March 1
(t = 59)?
b. Find the rate at which the daylight function changes.
c. Find the rate at which the daylight function changes on March 1.
Convert your answer to units of min/day and explain what
this result means.
d. Graph the function y = D′(t) using a graphing utility.
e. At what times of the year is the length of day changing most
rapidly? Least rapidly?
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