Question

The length of a rectangular playpen is two feet longer than its width. The areas for various widths are given in the table. Which type of function best models the area of the playpen as a function of the width? Width (feet) 2 Area (square feet) 8 3 15 4 24 5 35 linear exponential quadratic nana

Answer 1

$\begin{gathered} \text{Function = (n + 1)}^2\text{ - 1} \\ \\ \text{where n }\ge\text{ 2} \end{gathered}$

$\begin{gathered} (n+1)^2\text{ - 1} \\ (n\text{ + 1)(n + 1) - 1} \\ n^2\text{ + n + n + 1 - 1} \\ \text{Function = n}^2\text{ + 2n} \end{gathered}$

Final answer

$\text{The function n}^2\text{ + 2n is a quadratic function.}$