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 $f=-83x^{2}+654x + 618$ 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? according to the model, how many calories per day are needed by females between the ages of 4 and 8, inclusive, with this lifestyle? (type a whole number.) does the model underestimate or overestimate the number shown by the graph? by how much? the model $f=-83x^{2}+654x + 618$ the actual amount by approximately calories. (type a whole number.)

Explanation:

Step1: Determine the value of x

For age - group 4 - 8, we take the mid - point. The mid - point of 4 and 8 is $x=\frac{4 + 8}{2}=6$.

Step2: Substitute x into the model

Substitute $x = 6$ into the model $F=-83x^{2}+654x + 618$.
$F=-83\times6^{2}+654\times6 + 618$.
First, calculate $-83\times6^{2}=-83\times36=-2988$.
Second, calculate $654\times6 = 3924$.
Then $F=-2988+3924 + 618$.
$F=-2988+4542$.
$F = 1554$.

Step3: Compare with the graph value

From the graph, for females in the 4 - 8 age group, the number of calories is 1396.
Since $1554>1396$, the model overestimates the number.

Step4: Calculate the difference

The difference is $1554−1396 = 158$.

Answer:

According to the model, 1554 calories per day are needed. The model overestimates the actual amount by approximately 158 calories.