?The number of hours of daylight in a northeast city is modeled by the

Chapter 1, Problem 180

(choose chapter or problem)

The number of hours of daylight in a northeast city is modeled by the function

\(N(t)=12+3 \sin \left[\frac{2 \pi}{365}(t-79)\right]\)

where t is the number of days after January 1.

a. Find the amplitude and period.

b. Determine the number of hours of daylight on the longest day of the year.

c. Determine the number of hours of daylight on the shortest day of the year.

d. Determine the number of hours of daylight 90 days after January 1.

e. Sketch the graph of the function for one period starting on January 1.

Text Transcription:

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