Question

The bar graph shows the estimated number of calories per day needed to maintain energy balance forvarious gender and age groups for sedentary lifestyles. (Sedentary means a lifestyle that includes only thelight physical activity associated with typical day-to-day life.) The mathematical modelF= -82x² +654x+623 describes the number of calories needed per day, F, by females in age group x withsedentary lifestyles. According to the model, how many calories per day are needed by females between theages of 14 and 18, inclusive, with this lifestyle? Does this underestimate or overestimate the number shownby the graph? By how much?Calories Needed to Maintain Energy Balance for Sedentary Lifestyles3200 FemalesMalesGroup 3Group 42407Group 52195Group 2 2196Group 62400-Group 1,20041678 1807 19191847 17711600139817800-Calories per Day4-89-1314-18 19-30Age Range151931-50 51+

Answer 1

Given the bargraph below:

where the mathematical model:

`F=-82x^2+654x+623`

describes the number of calories needed per day by females in age group x with sedentary lifestyles.

To determine the number of calories per day needed by females between the ages of 14 and 18, we have

Where the red bar represents females and the yellow bar represents males.

Hence, the number of calories per day needed by females between 14 and 18, inclusive, with this lifestyle is

`1919`