The total time required to bake a loaf of bread, B, is a function of the temperature of the oven, T, and the size of the loaf, L. a) What is the total differential of this time-required-to-bake function? In other words, given B = f (T, L) what is dB? b) However, the size parameter, L, is really a function of two variables: M the mass of the loaf and A the average cross-sectional area of the loaf. What is the total differential for the time-required-to-bake function now? i.e. given B = f (T, M, A) what is dB? c) Following some experimentation, you determine the functional form of B is given by the expression below. In this expression, T, M, and A are the same as in b) and k is an experimentally measured constant. B = kMA2 / T2 1) Find the three partial derivatives for B. 2) Substitute the partial derivatives you found into the total differential from a) and provide a 1–2 sentence interpretation for this expression.
The total time required to bake a loaf of bread, B, is a function of the temperature of the oven, T, and the size of the loaf, L.
a) What is the total
b) However, the size parameter, L, is really a function of two variables: M the mass of the loaf and A the average cross-sectional area of the loaf. What is the total differential for the time-required-to-bake function now? i.e. given B = f (T, M, A) what is dB?
c) Following some experimentation, you determine the functional form of B is given by the expression below. In this expression, T, M, and A are the same as in b) and k is an experimentally measured constant.
B = kMA2 / T2
1) Find the three partial derivatives for B.
2) Substitute the partial derivatives you found into the total
differential from a) and provide a 1–2 sentence interpretation for
this expression.
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