the number of daylight hours for a particular day of the year is modeled by the

Question

the number of daylight hours for a particular day of the year is modeled by the formula belw, where D(t) is the number of daylight hours on day t of the year and K is a constant related to the total variation of daylight hours, latitude of the location and other factors.

note: you will need to consult a calendar in order to complete.

a) what is the vertical shift of this function? Explain what this represents in the context of the problem.

b) what is the period of this function? Explain what this represents in the context of the problem.

c) what is the horitzontal shift of this function? explain what this represents in the context of this problem. (Hint : what day is the 79th day of the year? what is the signifcance of the day?)

For detroit, Michigan, the constant K = 3

2a) use the function to determine how many hours of daylight detroit will receive on June 21st.

b) use the function to determine how many hours of daylight detroit will receive on Dec. 31.

Explanation / Answer

y = ksin[ 2pi/365(t -79 ] +12

a) vertical shift = 12

b) Period = 2pi/B Comparing with standardc sin function y = Asin(Bx +C)

Period = 2pi/(2pi/365) = 365

c) Horizontal shift = 79 towards right

On 70th day number of daylight hours is 12

d) daylight hours = 3sin[ 2pi/365(t -79 ] +12

t= 21 Daylight hours = 3sin[ 2pi/365(21-79) +12

= -2.52 +12 = 9.47 hours

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