Medicine—Pill Size: The Top Drug Company has developed a new type of pill in the shape of a ball. The spherical pill is dropped into a glass of water and dissolves. Tests show that when the 2-centimeter pill is dropped into the water, its radius decreases at an average rate of 0.003 centimeters per second.
(a) Write the radius r(t) as a function of time t. In this case, r(t) = 2 when t = 0.
(b) Knowing that the surface area of a sphere as a function of its radius is S(r) = 4πr2, simplify S(t) = S(r (t)), and interpret the meaning of this composition.
(c) Evaluate S(t) when t = 20 and interpret.
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