FUNCTIONS FROM TABLES, Part Three

A function contains the points shown in the table at right.

1. What kind of function does this appear to be? Write a possible equation.

   Hint (a):

   Is it linear or quadratic? Is it exponential? Or trigometric?

2. How does the function change?

   Steps (b):

   Compute the finite differences and look for a pattern.

3. Can you determine value of $f \left(0.5\right)$? Why or why not?

   Hint (c):

   Extend the pattern.

$\left. \begin{array} { c | c } { x } & { f ( x ) } \\ \hline 0 & { 1 } \\ { 1 } & { 5 } \\ { 2 } & { 25 } \\ { 3 } & { 125 } \\ { 4 } & { 625 } \end{array} \right.$