Question

Interpreting composite functions in the real world The volume of air in a balloon is represented by the function v(r)=4/3 ³, where r is the radius of the balloon, in
inches. The radius of the balloon increases with time, in seconds, by the function r(t) = 1/4 t².
Write a composite function that can be used to determine the volume of the balloon after t seconds. Then, select the
two true statements.

Answer 1

There are two true statements:

1. When the function is composed with r, the composite function is V(t) = (1/48) · π · t⁶.
2. V(r(6)) shows that the volume is 972π cubic inches after 6 seconds.

How to use composition between two function

Let be f and g two functions, there is a composition of f with respect to g when the domain of f is equal to the range of g. In this question, the domain variable of the function V(r) is replaced by substitution.

If we know that V(r) = (4/3) · π · r³ and r(t) = (1/4) · t², then the composite function is:

V(t) = (4/3) · π · [(1/4) · t²]³

V(t) = (4/3) · π · (1/64) · t⁶

V(t) = (1/48) · π · t⁶

There are two true statements:

1. When the function is composed with r, the composite function is V(t) = (1/48) · π · t⁶.
2. V(r(6)) shows that the volume is 972π cubic inches after 6 seconds.

To learn on composition between functions: brainly.com/question/12007574

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