a. $S=0.3x^3-2.8x^2+6.7x+30$ b. $S=31$; same as in the chart.
Work Step by Step
a. Simplify the function by combining like terms as follows: $S=0.2x^3+0.1x^3-1.5x^2-1.3x^2+3.4x+3.3x+25+5=0.3x^3-2.8x^2+6.7x+30$ b. For the age group of $45-54$, we have $x=5$ (group 5) and $S=0.3(5)^3-2.8(5)^2+6.7(5)+30=31$, which is exactly the same as the data shown in the chart.