# 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 *t*th 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.

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### 2 Answers

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.

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**