# A model for the number of hours of daylight (in hours) in Philadelphia on the tth day of the year is given by `L(t) = 12 + 2.8*sin(((2*pi)/365)*t - 80)` Use this to determine the change in the...

A model for the number of hours of daylight (in hours) in Philadelphia on the tth day of the year is given by `L(t) = 12 + 2.8*sin(((2*pi)/365)*t - 80)` Use this to determine the change in the number of hours of daylight on June 5 and June 15.

embizze | High School Teacher | (Level 1) Educator Emeritus

Posted on

The answer given by Justaguide is correct for the given equation. The given equation is wrong, in that it predicts a minimum June 21, while in the northern hemisphere it will be a maximum.

The graph of `12+2.8sin((2pi)/365t-80)` :

The graph of `12-2.8sin((2pi)/365t-80)` :

Using the second equation we get:

`L'(t)=(-5.6pi)/365cos((2pi)/365t-80)`

So `L'(156)=.01633` and `L'(166)=.00832`

So the daylight hours are increasing by the amount that justaguide indicated.

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The number of hours of daylight (in hours) in Philadelphia on the tth day of the year is given by the model as: `L(t) = 12 + 2.8 sin((2*pi)/365*t - 80)`

The change in daylight is given by L'(t)

`L'(t) = (5.6*pi/365)*cos(((2*pi)/365)*t - 80)`

June 5th is the 156th day of the year,

`L'(156) = (5.6*pi/365)*cos(((2*pi)/365)*156 - 80)`

=> -0.0163

June 15th is the 166th day of the year,

`L'(166) = (5.6*pi/365)*cos(((2*pi)/365)*166 - 80)`

=> -0.00831

The number of hours of daylight is decreasing by 0.0163 on June 5 and by 0.00831 on June 15