Finding the volume of a sphere that is increasing at a rate pro. to the recip of

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the radius... ? Can anyone help me with this problem?

At time t, t is greater than or equal to 0, the volume of a sphere is increasing at a rate of proportional to the reciprocal of its radius. At t=0, the radius of the sphere is 1 and at t=1, the radius is 2. (The volume of a sphere with radius r is V=4/3(pi)(r^3)

a. find the radius of the sphere as a function of t.
b. At what time t will the volume of the sphere be 27 times its volume at t=0?
 
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