The area of a circle is π΄(π)=ππ^{2}. The radius of a circular oil spill is increasing at a speed of 1/2 m per second.

a) Express the radius as a function of time

b) Find the composite function A(t)

c) When is the area 100pi m^2?

I'm having a tough time with this unit, I missed quite a bit of the lesson because my internet cut out.

(a)"The radius of a circular oil spill is increasing at a speed of 1/2 m per second." This can be interpreted as

\(\displaystyle \frac{dr}{dt}=\frac{1}{2}\) where \(\displaystyle t\) is the time in seconds.

This then gives

\(\displaystyle r = \frac{1}{2}t +c\)

Assuming that \(\displaystyle r=0\) when \(\displaystyle t=0\), then \(\displaystyle c=0\).

So \(\displaystyle r = \frac{1}{2}t\)

(b) You are given \(\displaystyle A(r)\). Use (a) to find \(\displaystyle A(t)\).

(c) Find \(\displaystyle t\) when \(\displaystyle A=100\pi\).

Show us what you can do for (b) and (c).