Question

In 2002, Political Action Committees (PAC's) contributed $282 million to federal candidates. By 2008, the figure had risen to 412.8 million. Let x be the number of years since 2000. Sketch a quick gragh. FInd a linear funtion that fits the data. In which year will the contributuons reach 900 million?

Answer 1

Let the required linear function be y = mx +c, where x is the number of years since 2000, m is the slope and c is the y-intercept. In 2002, Political Action Committees (PACs) contributed $ 282 million to federal candidates and 2008, the figure had risen to $ 412.8 million. Hence m = (412.8-282)/(8-2) = 130.8/6 = 21.8. Further, when x = 2, y = 282 so that 282 = (21.8)*2 +c or, c = 282-43.6 = 238.4. Thus, the required linear function is y = 21.8x +238.4. A graph of this line is attached.

When y = 900, we have 900 = 21.8x +238.4 or, 21.8x = 900-238.4 = 661.6 so that x = 661.6/21.8 = 30.35 (approximately). Hence, the contributions will reach $ 900 million in the year 2000+31 = 2031.