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=-81x^{2}+654x + 621 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 14 and 18, 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 14 and 18, inclusive, with this lifestyle? (type a whole number.)

Explanation:

Step1: Identify the age - group number

The age group of 14 - 18 is group 3. In the model, we assume \(x = 3\).

Step2: Substitute \(x = 3\) into the model

Substitute \(x = 3\) into \(F=-81x^{2}+654x + 621\).
\[

$$\begin{align*} F&=-81\times3^{2}+654\times3 + 621\\ &=-81\times9+1962+621\\ &=-729+1962 + 621\\ &=1233+621\\ &=1854 \end{align*}$$

\]

Step3: Compare with the graph value

From the graph, for females in the 14 - 18 age group, the number of calories is 1934.
The difference is \(1934 - 1854=80\). Since \(1854<1934\), the model underestimates the number shown by the graph.

Answer:

1854; The model underestimates the number shown by the graph by 80 calories.