Question

An oil slick is expanding as a circle. The radius of the circle is initially 3 meters and increases at the rate of 15 meters per day. Express the area of the circle as afunction of t, the number of days elapsed. The area of a circle is A(r) = 3.14r^2

Answer 1

So, we know that the area of a circle is given by the function:

$A(r)=3.14r^2$

So, if we notice, the radius increase at the rate of 15 meters per day, then, the radius of the oil stick after t days is given by:

r=3+15t.

And, we can rewrite:

$A(t)=3.14(3+15t)^2$

So,

$A(t)=3.14(9+90t+225t^2)$

And that is the area of the circle as a function of t.