Question

the bar graph shows the estimated number of calories per day needed to maintain energy balance for various gender and age groups for moderately active lifestyles. moderately active means a lifestyle that includes physical activity equivalent to walking 1.5 to 3 miles per day at 3 to 4 miles per hour, in addition to the light physical activity associated with typical day - to - day life. complete parts a. through c.
a. the mathematical model below describes the number of calories needed per day, w, by women in age group x with moderately active lifestyles.
w = - 66x² + 526x + 1030
according to the model, how many calories per day are needed by women over the age of 51, with this lifestyle?
w = 1810 calories
does this underestimate or overestimate the number shown by the graph? by how much?
the model underestimates the number shown by the graph by calorie(s).

Explanation:

Step1: Identify age - group value

For women over 51, we assume \(x = 6\) (assuming age - groups are numbered 1 - 6 and the last one is for 51+).

Step2: Substitute into the formula

Substitute \(x = 6\) into \(W=-66x^{2}+526x + 1030\).
\[

$$\begin{align*} W&=-66\times6^{2}+526\times6 + 1030\\ &=-66\times36+3156+1030\\ &=-2376+3156+1030\\ &=780 + 1030\\ &=1810 \end{align*}$$

\]
From the graph, for women in the 51+ age - group, the number of calories is 2000.

Step3: Calculate the difference

The difference is \(2000 - 1810=190\).

Answer:

The model underestimates the number shown by the graph by 190 calorie(s).