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Question

# The basal energy requirement for an individual indicates the minimum number of calories necessary to maintain essential life-sustaining processes such as circulation, regulation of body temperature, and respiration. Given a person's sex, weight $w$ (in kilograms), height $h$ (in centimeters), and age $y$ (in years), we can estimate the basal energy requirement in calories using the following formulas, where $C_f$ and $C_m$ are the calories necessary for females and males, respectively:\begin{aligned} C_f &=66.5+13.8 w+5 h-6.8 y \\ C_m &=655+9.6 w+1.9 h-4.7 y \end{aligned}(a) Determine the basal energy requirements first for a $25$-year-old female weighing $59$ kilograms who is $163$ centimeters tall and then for a $55$-year-old male weighing $75$ kilograms who is $178$ centimeters tall.(b) Discuss why, in both formulas, the coefficient for $y$ is negative but the other coefficients are positive.

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#### (a)

First we will calculate basal energy requirement in calories for female who is $25$ years old, weighing $59kg$ and who is $163cm$ tall.

\begin{align*} C_f&=66.5 + 13.8 \cdot 59 + 5\cdot 163 - 6.8 \cdot 25\\\\ &=66.5 + 814.2 + 815 -170\\\\ &=1525.7 \hspace{0.1cm}calories \end{align*}

Now we will calculate basal energy requirement in calories for male who is $55$ years old, weighing $75kg$ and who is $178cm$ tall.

\begin{align*} C_f&=655 + 9.6 \cdot 75 + 1.9\cdot 178 - 4.7 \cdot 55\\\\ &=655 + 720 + 338.2 - 258.5\\\\ &=1454.7 \hspace{0.1cm}calories \end{align*}

#### (b)

As people age, their basal energy requirement is decreasing, that is why $y$ coefficient is always negative $(-)$. Other two coefficients are getting bigger as person is $\text{\underline{taller}}$ and $\text{\underline{heavier}}$. It is logical that larger people in general need more calories to move and maintain basic body function because of larger muscles.

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