A person's basal metabolic rate (BMR) is the minimal number...

A person's basal metabolic rate (BMR) is the minimal number of daily calories needed to keep their body functioning at rest. The BMR (in kcal/day) of a man of mass $m(\text { in } \mathrm{kg}),$ height $h$ (in $\mathrm{cm}$ ) and age $a$ (in years) can be approximated by $^{12}$ $$P=f(m, h, a)=14 m+5 h-7 a+66$$ and for women by $$P=g(m, h, a)=10 m+2 h-5 a+655$$ (a) What is the BMR of a 28 -year-old man $180 \mathrm{cm}$ tall weighing $59 \mathrm{kg} ?$ (b) What is the BMR of a 43 -year-old woman $162 \mathrm{cm}$ tall weighing $52 \mathrm{kg} ?$ (c) Describe the level surface $P=2000$ for a woman and explain what the points on this level surface represent. (d) If a 40 -year-old man 175 cm tall weighing 77 kg restricts himself to a diet with a daily caloric intake of 1600 kcal, should he expect to lose weight?

A person's basal metabolic rate (BMR) is the minimal number of daily calories needed to keep their body functioning at rest. The BMR (in kcal/day) of a man of mass $m(\text { in } \mathrm{kg}),$ height $h$ (in $\mathrm{cm}$ ) and age $a$ (in years) can be approximated by $^{12}$
$$P=f(m, h, a)=14 m+5 h-7 a+66$$
and for women by
$$P=g(m, h, a)=10 m+2 h-5 a+655$$
(a) What is the BMR of a 28 -year-old man $180 \mathrm{cm}$ tall weighing $59 \mathrm{kg} ?$
(b) What is the BMR of a 43 -year-old woman $162 \mathrm{cm}$ tall weighing $52 \mathrm{kg} ?$
(c) Describe the level surface $P=2000$ for a woman and explain what the points on this level surface represent.
(d) If a 40 -year-old man 175 cm tall weighing 77 kg restricts himself to a diet with a daily caloric intake of 1600 kcal, should he expect to lose weight?

Key Concepts

Basal Metabolic Rate (BMR)

Basal Metabolic Rate represents the minimal number of calories required by the body to maintain essential functions at rest over a day. It is a measure of energy expenditure that takes into account personal physical attributes such as mass, height, and age, and is crucial for understanding the minimum caloric needs for sustaining life without additional activity.

Linear Function Models

Linear function models use linear equations to approximate relationships between variables. In contexts like estimating BMR, these models allow the prediction of a response (such as calorie requirement) based on inputs like mass, height, and age. This approach simplifies complex biological phenomena into manageable mathematical equations for analysis and prediction.

Level Surface (Level Set)

A level surface (or level set) in the context of a function of multiple variables is the collection of all points where the function takes on the same constant value. In practical applications, such as caloric models, points on a level surface represent different combinations of input variables that yield the same output, thereby providing insight into how different factors may balance to achieve a specified caloric need.

Energy Balance

Energy balance refers to the relationship between caloric intake and caloric expenditure within the body. It is the principle underlying weight maintenance, loss, or gain. When intake is less than the expenditure (which includes basal metabolic rate and physical activity), the body is expected to lose weight, whereas a surplus leads to weight gain. This concept is integral to dietary planning and managing metabolic health.

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