Answer:
B. quadratic
Step-by-step 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.
[tex]\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}[/tex]
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.
