Question

the bar graph shows the estimated number of calories per day needed to maintain energy balance for various gender and age groups for sedentary lifestyles (sedentary means a lifestyle that includes only the light physical activity associated with typical day - to - day life). the mathematical model f=-83x^{2}+653x + 623 describes the number of calories needed per day, f, by females in age group x with sedentary lifestyles. according to the model, how many calories per day are needed by females between the ages of 9 and 13, inclusive, with this lifestyle? does this underestimate or overestimate the number shown by the graph? by how much? according to the model, how many calories per day are needed by females between the ages of 9 and 13, inclusive, with this lifestyle? (type a whole number.)

Explanation:

Step1: Identify the age - group value

The age - group of 9 - 13 is considered as group \(x = 2\) (assuming groups are numbered 1, 2, 3, etc. starting from the first age - group).

Step2: Substitute \(x = 2\) into the formula

The formula for the number of calories \(F=-83x^{2}+653x + 623\). Substitute \(x = 2\) into it:

$$
LATEXBLOCK0
$$

Step3: Compare with the graph value

From the graph, for females in the 9 - 13 age - group, the number of calories is 1803. Since \(1597<1803\), it is an underestimate.

Step4: Calculate the difference

The difference is \(1803 - 1597=206\).

Answer:

1597; underestimate; 206