A carton of milk has spilled on a tile floor. The milk flow can be expressed with the function m(t) = 9t, where t represents time in minutes and m represents how far the milk is spreading.

The flowing milk is creating a circular pattern on the tile. The area of the pattern can be expressed as A(m) = πm2.

Part A: Find the area of the circle of spilled milk as a function of time, or A[m(t)]. Show your work. (6 points)

Part B: How large is the area of spilled milk after 2 minutes? You may use 3.14 to approximate π in this problem. (4 points)

The area of circle of spilled milk as a function of time, or A[m(t)] is [tex]A[m(t)]=81t^2\pi[/tex]. The area of spilled milk after 2 minutes is 1017.36 square unit.

Step-by-step explanation:

Consider the provided information.

The milk flow can be expressed with the function m(t) = 9t, where t represents time in minutes and m represents how far the milk is spreading.

The area of the pattern can be expressed as A(m) = πm².

Part A:

To find the area of the circle of spilled milk as a function of time, substitute the value of function in area as shown:

[tex]A(m)=\pi m^2[/tex]

[tex]A[m(t)]=\pi (9t)^2[/tex]

[tex]A[m(t)]=81t^2\pi[/tex]

Hence. the area of circle of spilled milk as a function of time, or A[m(t)] is [tex]A[m(t)]=81t^2\pi[/tex].

Part B:

Substitute t = 2 in the above equation.

[tex]A[m(t)]=81(2)^2\pi[/tex]

[tex]A[m(t)]=81\times 4\times 3.14[/tex]

[tex]A[m(t)]=1017.36[/tex]

Hence, the area of spilled milk after 2 minutes is 1017.36 square unit.