(a) Which releases the most energy when metabolized, \(1 \mathrm{~g}\) of carbohydrates or \(1 \mathrm{~g}\) of fat? (b) A particular chip snack food is composed of \(12 \%\) protein, \(14 \%\) fat, and the rest carbohydrate. What percentage of the calorie content of this food is fat? (c) How many grams of protein provide the same fuel value as \(25 \mathrm{~g}\) of fat?

To determine which releases the most energy when metabolized, we can simply compare the calorie values of carbohydrates and fats: Carbohydrates: 1 gram = 4 calories Fats: 1 gram = 9 calories Since 9 calories (from fats) is greater than 4 calories (from carbohydrates), 1 gram of fat releases more energy when metabolized than 1 gram of carbohydrates.

We have the following information about the food product: - 12% protein - 14% fat - The rest carbohydrate Let's first find the percentage of carbohydrates in the food product: 100% - 12% (protein) - 14% (fat) = 74% carbohydrates Now, we'll calculate the calorie contribution of each component (protein, fat, and carbohydrates) per 100 grams of the food product: Protein: \(0.12 \times 100 \mathrm{~g} \times 4 \mathrm{~cal/g} = 48 \mathrm{~cal}\) Fat: \(0.14 \times 100 \mathrm{~g} \times 9 \mathrm{~cal/g} = 126 \mathrm{~cal}\) Carbohydrates: \(0.74 \times 100 \mathrm{~g} \times 4 \mathrm{~cal/g} = 296 \mathrm{~cal}\) Total calorie content: \(48 \mathrm{~cal} + 126 \mathrm{~cal} + 296 \mathrm{~cal} = 470 \mathrm{~cal}\) To find the percentage of the calorie content that is fat, calculate the proportion of fat calories to the total calorie content: Fat percentage: \(\frac{126 \mathrm{~cal}}{470 \mathrm{~cal}} \times 100\% \approx 26.8\%\) Thus, approximately 26.8% of the calorie content in this food product is fat.

First, we calculate the fuel value provided by 25 grams of fat: 25 grams of fat: \(25 \mathrm{~g} \times 9 \mathrm{~cal/g} = 225 \mathrm{~cal}\) Next, we determine how many grams of protein provide the same fuel value (225 calories): Let x = grams of protein \(x \times 4 \mathrm{~cal/g} = 225 \mathrm{~cal}\) Solve for x: \(x = \frac{225 \mathrm{~cal}}{4 \mathrm{~cal/g}} = 56.25 \mathrm{~g}\) Therefore, 56.25 grams of protein provide the same fuel value as 25 grams of fat.