Question

A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 5t, where t represents time in minutes and p represents how far the paint is spreading. The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(p) = πp2. Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work. (6 points) Part B: How large is the area of spilled paint after 2 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Answer 1

Because we know the area in terms of paint flow, and paint flow in terms of time, we can substitute p(t) for p in the A(p) equation.

A(p(t)) = A(t) = π * (5t)^2 (assuming it's squared for the A(p).
B: 314 units^2

If A(p) = πp2 (instead of p^2), then A(t) = 10πt
B: 31.4 units^2

Answer 2

A). A[p(t)] = 25πt²

B). 314 square unit

Explanation:

A bucket of paint on a tile floor. The paint flow can be expressed with the function p(t) = 5t

where t represents the time and p represents how far the paint will flow.

Area of the pattern can be expressed as A(p) = πp²

A). Area of the circle of spilled paint can be defined as A[p(t)] = π(5t)²

A[p(t)] = 25πt²

B). In this part we have to calculate the area of spilled paint after 2 minutes.

A[p{2)] = 25π(2)²

= 100π

= 100(3.14)

= 314 square unit