Thinking Mathematically (6th Edition)

The number of calories needed between the age of 19 and 30 are $2332$. It underestimates the number shown by the graph by $68$calories.
Consider the equation as follows: $M=-96{{x}^{2}}+802x+660$ where M represents the number of males and x represents the age group. Now, substitute the value of $x$as 4 and find the value of$F$. \begin{align} & M=-96{{x}^{2}}+802x+660 \\ & =-96{{\left( 4 \right)}^{2}}+802\left( 4 \right)+660 \\ & =-1536+3208+660 \\ & =2332 \end{align} Here, x is considered as 4 because the age group 19-30 lies in the group 4. From the graph, $2400$calories are needed for males of age group, 19-30. Now, subtract the value of the calorie against age range 19-30 given in the graph from the calculated value of the calorie to obtain: $2400-2332=68$ The value of graph is higher by 68 calories. Hence, the given model underestimates the number shown by the graph by $68$ calories.