Question

A homeowner looked at her electric bill over the past six months and noticed that the bill has been increasing as is shown in the picture.

Which type of function best models the homeowner’s electric bill over the past six months?
A. exponential
B. quadratic
C. linear
D. cubic

Answer 1

B. quadratic

Explanation:

One way to decide without a graph if a function is linear, quadratic, or exponential. is to take the first, second, and third differences between the terms

If the

• First differences are constant, the function is linear.
• Second differences are constant, the function is quadratic.
• Third differences are constant, the function is cubic.
• Fourth differences are NOT constant, the function may be exponential.

`\begin{array}{ccccl}\textbf{Month} & \textbf{Bill/\$} & \textbf{1st Diff} & \textbf{2nd Diff}\\\text{Aug} & 64.20 & & \\ & & 3.21 & \\\text{Sept} &67.41 & & 0.17\\ & &3.38 & \\\text{Oct} &70.79& & 0.13\\ & & 3.51 &\\ \text{Nov}&74.30& & 0.21\\ & & 3.72 & \\\text{Dec} &78.02 & & 0.20\\ & & 3.92 & \\\text{Jan} &81.94 & & \\\end{array}`

The first differences are not constant, so the function is not linear.

The second differences are constant (hovering around $ 0.18 each), so the function is quadratic.

The graph below shows that the points give an excellent fit to a quadratic function.