At time t, t $\displaystyle \ge$ 0, the volume of a sphere is increasing at a rate proportional to the reciprocal of its radius. At t = 0, the radius of the sphere is 1 and at t = 15, the radius is 2. (Volume of sphere is V = 4/3pir^3)

a) Find the radius of the sphere as a fuction of t

b) at what time t will the volume of the sphere be 27 times its volume @ t= 0?