Two students each write a function, S(n)
, that they think can be used to find the number of squares needed to make the n
th figure in the pattern shown.

Use the drop-down menus to explain why each function does or does not represent the number of squares needed to make the n
th figure in the pattern.

Shara: S(1) = 2

S(n) = S(n − 1) ⋅ 2
This function
be used to find the number of squares needed to make the n
th figure in the pattern.

The number of squares needed to make each figure is
the number of squares used in the previous figure.

Darren: S(n) = 2n
This function
be used to find the number of squares needed to make the n
th figure in the pattern.

The first figure has 2 squares, and you multiply by
each time a figure is added. This repeated multiplication can be represented by an exponet