A ball is being inflated at a rate that can be modeled by the function cap v times t is equal to 10 t , where t is the number of seconds spent inflating the ball. The radius at a given volume can be modeled by the function r times cap v is equal to cube root of 3 cap v over 4 pi Which composite function can be used to determine the radius of the ball depending on the number of seconds spent inflating the ball?
Answer
A
r times open paren cap v times t close paren is equal to 10 cube root of 30 cap v over 4 pi
B
r times open paren cap v times t close paren is equal to cube root of 30 t over 4 pi
C
r times open paren cap v times t close paren is equal to 10 cube root of 3 cap v over 4 pi
D
r times open paren cap v times t close paren is equal to 10 cube root of 3 t over 4 pi
Explanation
To find the radius after t seconds, substitute the volume function V(t) = 10t into r(V) = ∛(3V/(4π)). This gives r(V(t)) = ∛(3(10t)/(4π)) = ∛(30t/(4π)). Choice B gives this composite function.
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