Question

hw07-obj-a6: problem 5
problem value: 1 point(s). problem score: 0%. attempts remaining: 3 attempts.
(1 point) suppose r = f(t) is the radius, in centimeters, of a circle at time t minutes, and a(r) is the area, in square centimeters, of a circle of radius r centimeters.
which of the following statements best explains the meaning of the composite function a(f(t))?
a. the area of a circle, in square centimeters, at time t minutes.
b. the radius of a circle, in centimeters, at time t minutes.
c. the area of a circle, in square centimeters, of radius r centimeters.
d. the function f of the minutes and the area.
e. none of the above

Explanation:

The function $r = f(t)$ gives the radius of a circle at time $t$. The function $A(r)$ gives the area of a circle with radius $r$. When we form the composite function $A(f(t))$, we first find the radius $r$ at time $t$ using $f(t)$ and then find the area of the circle with that radius using $A(r)$. So $A(f(t))$ represents the area of the circle at time $t$.

Answer:

A. The area of a circle, in square centimeters, at time $t$ minutes