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+655x + 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 4 and 8, inclusive, with this lifestyle? does this underestimate or overestimate the number shown by the graph? by how much? 1195 (type a whole number.) does the model underestimate or overestimate the number shown by the graph? by how much? the model f = - 83x^2+655x + 623 the actual amount by approximately calories. (type a whole number.)

Explanation:

Step1: Identify the age - group number

The age range 4 - 8 is group 1, so \(x = 1\).

Step2: Substitute \(x\) into the formula

Substitute \(x = 1\) into \(F=-83x^{2}+655x + 623\). Then \(F=-83\times1^{2}+655\times1+623\).
First, calculate \(-83\times1^{2}=-83\). Then \(655\times1 = 655\).
So \(F=-83 + 655+623\).
\(F=1195\).

Step3: Compare with the graph value

From the graph, for females in the 4 - 8 age range, the number of calories is 1225.
Since \(1195<1225\), the model underestimates the actual amount.

Step4: Calculate the difference

The difference is \(1225 - 1195=30\).

Answer:

The model \(F=-83x^{2}+655x + 623\) underestimates the actual amount by approximately 30 calories.