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 year is the length of day changing most rapidly? Least rapidly?

Transcribed Image Text:

"2т (t + 10) D(t) = 12 – 3 cos 365