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 includes only the light physical activity associated with typical day - to - day life.) the mathematical model f = - 82x²+653x + 621 describes the number of calories needed per day for 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 the model 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? 1192 (type a whole number.) does the model underestimate or overestimate the number shown by the graph? by how much? the model f = - 82x²+653x + 621 overestimates the actual amount by approximately calories. (type a whole number.)

Explanation:

Step1: Determine the value of x

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

Step2: Substitute x into the model

Substitute $x = 6$ into the model $F=-82x^{2}+653x + 621$.
$F=-82\times6^{2}+653\times6+621$.
First, calculate $-82\times6^{2}=-82\times36=-2952$.
Then, calculate $653\times6 = 3918$.
Now, $F=-2952+3918+621$.
$F=-2952+(3918 + 621)=-2952+4539=1587$.
Let's assume the value from the graph is 1192.

Step3: Calculate the difference

The difference between the model value and the graph value is $1587-1192 = 395$.

Answer:

395