In a trend that scientists attribute, at least in part, to global warming, a certain floating cap of sea ice has been shrinking since 1980 . The ice cap always shrinks in the summer and grows in winter. Average minimum size of the ice cap, in square miles, can be approximated by $A=\pi r^{2}$. In 2013 , the radius of the ice cap was approximately $766 \mathrm{mi}$ and was shrinking at a rate of approximately $4.4 \mathrm{mi} / \mathrm{yr}$. How fast was the area changing at that time?

Step 1 ：The problem is asking for the rate of change of the area of the ice cap. This is a problem of related rates. We know the formula for the area of a circle is \(A=\pi r^{2}\), and we are given the rate of change of the radius, \(\frac{dr}{dt} = -4.4 \, \text{mi/yr}\) (negative because the radius is shrinking), and the radius at the time we are interested in, \(r = 766 \, \text{mi}\). We want to find \(\frac{dA}{dt}\), the rate of change of the area.

Step 2 ：We can find this by differentiating the area formula with respect to time, and then substituting the given values.

Step 3 ：Taking the derivative of \(A=\pi r^{2}\) with respect to time gives \(\frac{dA}{dt} = 2\pi r \frac{dr}{dt}\).

Step 4 ：Substituting the given values, \(r = 766 \, \text{mi}\) and \(\frac{dr}{dt} = -4.4 \, \text{mi/yr}\), into the equation gives \(\frac{dA}{dt} = 2\pi (766) (-4.4)\).

Step 5 ：Solving this equation gives \(\frac{dA}{dt} = -6740.8\pi \, \text{mi}^{2}/\text{yr}\).

Step 6 ：\(\boxed{-6740.8\pi \, \text{mi}^{2}/\text{yr}}\) is the rate of change of the area of the ice cap in 2013.