Question

A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 6(t), 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) = 3.14(p)^2

Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work.

Part B: How large is the area of spilled paint after 8 minutes? You may use 3.14 to approximate pi in this problem.

Answer 1

A) From the function p(t)=6(t), we know that p is 6t, so we plug this into it, to get 3.14 * (6t)^2, or 113.04t^2.

B) Using what we got from A), we plug it in and get 113.04 * 8 * 8, or 7234.56 (Use a calculator on this, or just bash it with pencil and paper).

Answer 2

A(p(t)) =113.04 t^2

A (p(8)) =7234.56

Explanation:

p(t) = 6t

A (p) = 3.14 p^2

So A(p(t)) = means we put p(t) in the function for A

= 3.14 p^2

= 3.14 (6t) ^2

= 3.14 (36t^2)

A(p(t)) =113.04 t^2

Let t=8

A (p(8)) = 113.04 (8)^2

= 113.04(64)

=7234.56