To predict the crude steel production in the year 2008, first, you have to determine the value of x to use.
If 1980 is considered year zero (x=0), then you have to calculate the difference between 2008 and 1980 to determine the value of x:
[tex]2008-1980=28[/tex]
Counting from 1980 up, the year 2008 is the 28th year.
Next, replace the function with x=28 and calculate the value of f(x)
[tex]\begin{gathered} f(x)=-0.167x^2+2.833x+80 \\ f(28)=-0.167(28)^2+2.833\cdot28+80 \end{gathered}[/tex]
Solve the exponent, then the multiplications, and finally the additions:
[tex]\begin{gathered} f(28)=-0.167\cdot784+79.324+80 \\ f(28)=-130.26+79.324+80 \\ f(28)=29.064 \end{gathered}[/tex]
The crude steel production in 2008 will be 29.064.
