Question

A drop of oil makes a circular ring in a water puddle. The radius of the oil ring expands at 1.5 cm per second. If r(t)=1.5t and a(r)=лr^2, what composition of function describes the area of the oil ring in terms of time?

Answer 1

Answer:

$a(t) =n(0.25t^2)$

Step-by-step explanation:

Given

$r(t) = 0.5t$

$a(r) = nr^2$

Required

Determine the area in terms of time

From the question, we have:

$r(t) = 0.5t$ -> radius per time

and

$a(r) = nr^2$ --> area from radius

The interpretation of the question is to find the composite function: a(t)

If $a(r) = nr^2$, and $r(t) = 0.5t$, the

Substitute 0.5t for r

$a(t) =n(0.5t)^2$

$a(t) =n*0.25t^2$

$a(t) =n(0.25t^2)$