r = ∛(3V/(4π)) = ∛(3(12+20t)/(4π)) = ∛(3(3+5t)/π)
∛(3(3+5t)/π) = 16
3(3+5t)/π = 4096
3+5t = 4096π/3
t = (4096π - 9)/15
The radius r, in inches, of a spherical balloon is related to the volume V by r(V)= cubed√3V/4pi
Air is pumped into the balloon so the volume after t seconds is given by V(t)=12+20t.
a. Find the expression for the composite function r(V(t)).
b. What is the exact time in seconds when the radius reaches 16 inches?
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