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+616 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 the ages of 19 and 30, inclusive, with this lifestyle? Does this underestimate or overestimate the number shown by the graph? By how much?

Answer 1

ANSWERS

F = 1920 calories

The model overestimates the number shown in the graph by 75 calories.

Step-by-step explanation

The model used to estimate the number of calories needed per day by females in age group x is,

`F=-82x^2+654x+616`

We have to find how many calories are needed by females between the ages of 19 and 30. This age group is group 4, so we have to find F for x = 4,

`F(4)=-82\cdot4^2+654\cdot4+616=1920`

Hence, the females between 19 and 30 years old need 1920 calories.

In the graph, the calories needed by females are represented by the red bars. For group 4, the calories needed are 1845, which is less than the estimated by the model. Hence, the model overestimates the number shown by the graph by 75 calories.