Answer
57 new contracts
Work Step by Step
Step 1: Let $x$ = years after 2001; and $y$ = the number of contracts (It may be helpful to graph this, to visualize the growth in contracts).
This gives the points (2, 15) and (8, 33); because there were 15 new contracts in 2003 (which is 2 years after 2001) and 33 new contracts in 2009 (which is 8 years after 2001).
Step 2: Use this information to write out the slope of equation
$m$ = $\frac{y_{2}-{y_1}}{x_{2}-x_{1}}$
$m$ = $\frac{33 - 15}{8 - 2}$
$m$ = $\frac{18}{6}$ = 3
Step 3: Next use the point-slope formula to write the equation
$y$ - $y_{1}$ = $m$($x$ - $x_{1}$)
$y$ - 15 = 3($x$ - 2)
$y$ -15 = 3$x$ - 6
$y$ = 3$x$ + 9
Step 4: Using this equation we can predict how many new contracts there will be in 2017 to fill the point (16, $y$)
$y$ = 3(16) + 9 = 57
