Question

Can someone please help me answer this!!!

A circular oil spill continues to increase in size. The radius of the oil spill, in miles, is given by the function r(t) = 0.5 + 2t, where t is the time in hours. The area of the circular region is given by the function A(r) = πr2, where r is the radius of the circle at time t.


Explain how to write a composite function to find the area of the region at time t.

Answer 1

So what's the problem Abs?
Just take your r function and stick it into A, ya?\[\large\rm A=\pi\color{orangered}{r}^2\]\[\large\rm A=\pi\color{orangered}{(0.5+2t)}^2\]

Answer 2

so would I have to solve that?

Answer 3

No. That's all you need to do.
Unless they want you to expand out the square.
That seems unnecessary though.

You need to explain what "you" did though.
So maybe say something like,
"Take the composition A(r(t)), replacing the r in A(r) with the function r(t)."

Answer 4

I dunno, it's a weird question :d
Just seems like one simple step.

Answer 5

Oh okay thanks