quadratic word problem

Question

  Year: 1980        1985       1990       1995                                         1           18.8          22.6         26.0        29.0                                 The table lists the amount of emmissions of a certain pollutant in millions of tons.  If the amount of the emissions is modeled by f(x)=ax+bx+c where x is the year estimate the amount of emmissions in 2030.

Answer 1

                           1980²   1980   1                         18.8 
(3x3 Matrix) →     1985²   1985   1     ×   X    =       22.6
                           1990²   1990   1                         26.0 

                                   a                       0 
(3x1 Matrix) →  X   =    b      =              32.48       
                                   c               -32 928.40 

 f(2030) = 0 · 2030² + 32.48 · 2030 - 32928.40
The amount of emissions in 2030 is 33.0 tons