Once again we are going to use the equation of oscillations:

Note that by using 365 in the denominator we will be able to use t in days instead of months.

Here is a look at our raw data for this problem:

With the average sunset time M = 6.5417 which is about 6:32.

Plotting the raw data gives the following graph:

We then use our transformation functions:

Now that we have transformed our raw data, we can then plug it into Matlab and obtain the following values for our linear regression formula y = a + bt.

a = -.8678 b = .3265

which gives the regression line:

This equation gives the following graph

Going back to our original equation we can model the sunset time with the approximating function:

As an additional bonus, our problem told us that on June 15 (t = 166 days) the sunset time was 7:49. To test our approximating function we can plug in t = 166 and see how exact our function is.

Solving for y, the sunset time, gives:

As we can see our approximating function is right on target.