The relationship between the amount of calories consumed in food and the amount of calories expended through metabolism and physical activity is known as
a. body mass index.
b. energy balance.
c. metabolic rate.
d. metabolic equivalent.

This relationship is known as the energy balance - b. If we were talking about the metabolic rate we would have to exclude the porton which talks about the physical activity. Whne talking about the metabolic rate for example we would only talk about the baseline metabolic activity and the amount of calories someone takes in. For that reason B is correct.