Question

A container of oil has spilled on a concrete floor. The oil flow can be expressed with the function n(t) = 7t, where t represents time in minutes and n represents how far the oil is spreading. The flowing oil is creating a circular pattern on the concrete. The area of the pattern can be expressed as A(n) = πn2. Part A: Find the area of the circle of spilled oil as a function of time, or A[n(t)]. Show your work. (6 points) Part B: How large is the area of spilled oil after 8 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Answer 1

Part A.
The notation: A(n(t)) is saying to put function n(t) in for n in A(n).

A(t) = (pi)(7t)^2
A(t) = 49(pi)t^2

part B.
A(8), put in t = 8
A = 49(pi)(8)^2
A = 9847