Tuesday, May 13, 2014

My Calculus Class's Final Published Work: Rate of Change of the the Sun Setting Throughout the Year.

We studied the sunsets for the years 2012 and 2013. We graphed two dates, the 1st and the 15th, from each month for the two years. This is what we found:

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 


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