Answer:
The area at time t is given by [tex]A(t) =\pi (4t^2+2t+0.25).[/tex]
Step-by-step explanation:
We know the radius [tex]r(t)[/tex] of the oil spill as a function of time, and we know the area [tex]A(r)[/tex] as a function of radius, and we want the area at time t. In other words we are looking for area as a function of time [tex]A(t)[/tex]
We find [tex]A(t)[/tex] by putting [tex]r(t)[/tex] into [tex]A(r)[/tex] as a substitute to r:
[tex]A(t) = A(r(t))= \pi r(t)^2 =\pi (0.5 + 2t)^2={\pi (4t^2+2t+0.25).}[/tex]
[tex]\boxed{A(t) =\pi (4t^2+2t+0.25).}[/tex]
Which is our answer.
