Question

A ball is being inflated at a rate that can be modeled by the function V(t) = 10t, where t is the number of seconds spent inflating the ball. The radius at a given volume can be modeled by the function . Which composite function can be used to determine the radius of the ball depending on the number of seconds spent inflating the ball?

Answer 1

Answer:

∛(7.5t/π)

Step-by-step explanation:

Since the volume of the sphere V(t) at any time, t is V(t) = 10t. We also know that the volume of a sphere V(r) with radius, r is V(r) = 4/3πr³. Equating the two expressions, V(r) = V(t)

4/3πr³ = 10t

r³ = 10t × 3/4π

r³ = 30t/4π

r³ = 7.5t/π

r = ∛(7.5t/π)