x=0 represents Jan. 1st 2012

x=1 represents Jan. 15th 2012

x=2 represents Feb. 1st 2012

.........

x=48 represents Dec. 15th 2013

Then we looked at the graph and came up with an equation:

f(x)= 1.5sin(π/12(x-66/π))+7

or

f(x)= 1.5cos(π/12*x)+7

To find the rate of change we derived the equation and got:

f '(x)=.3927sin (π/12*x)

So the rate of chance of the sunsets on May 15th 2014 is:

x=58 y=0.19635 min/day