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

Given:
Oil flow: n(t) = 7t  where t is time and n = how far the oil is spreading
Area of the circular pattern the oil is forming:
A(n) = πn²


Part A: Find the area of the circle of spilled oil as a function of time, or A[n(t)]

A[n(t)] = π (7t)² = π * 49 * t²

How large is the area of spilled oil after 8 minutes? 

n(t) = 7t → 7 * 8 = 56

A(56) = 3.14 * 56² = 9,847.04 square units

or

A[n(t)] = π (7t)² 
A[n(8)] = 3.14 * (7*8)² = 3.14 * 3,136 = 9,847.04 square units