A circular oil slick is expanding with radius, r in feet, at time t in hours given by r=12t−0.3t^2, for t in hours, 0≤t≤10.

Find a formula for A=f(t), the area of the oil slick as a function of time.

gee - impatient much?

typed the wrong questoin

To find a formula for the area of the oil slick as a function of time, we need to use the formula for the area of a circle: A = πr^2, where A is the area and r is the radius.

In this case, the radius of the oil slick is given by r = 12t - 0.3t^2. So, we can substitute this expression for r into the formula for the area:

A = π(12t - 0.3t^2)^2

Simplifying this expression further, we can expand and simplify:

A = π(144t^2 - 7.2t^3 + 0.09t^4)

Therefore, the formula for A as a function of time, f(t), is:

f(t) = 144πt^2 - 7.2πt^3 + 0.09πt^4