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

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

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)`