Answer
a. $S=-0.03x^3+0.2x^2+2.3x+24$
b. underestimates by $0.25$
Work Step by Step
a. Simplify the expression by combining like terms:
$S=-0.02x^3-0.01x^3+0.4x^2-0.2x^2+1.2x+1.1x+22+2=-0.03x^3+0.2x^2+2.3x+24$
b. The slightly conservative political identification group corresponds to $x=5$ (group 5); we have $S=-0.03(5)^3+0.2(5)^2+2.3(5)+24=36.75$ and we can get a value of $37$ from the chart. Thus the model underestimates the score by $37-36.75=0.25$.
