The learning rate for new skills is proportional to the difference between the maximum potential for learning that skill, M, and the amount of the skill already learned, L. Which equation describes this relationship? Choose 1 answer: (A) L(t)=(k)/((M-L)) (B) L(t)=k(M-L) (C) (dL)/(dt)=k(M-L) (D) (dL)/(dt)=(k)/((M-L))

Question

The learning rate for new skills is proportional to the difference between the maximum potential for learning that skill,  M, and the amount of the skill already learned,  L. Which equation describes this relationship? Choose 1 answer: (A)  L(t)=(k)/((M-L)) (B)  L(t)=k(M-L) (C)  (dL)/(dt)=k(M-L) (D)  (dL)/(dt)=(k)/((M-L))

Bytelearn · Accepted Answer

Understanding the Problem: The problem states that the learning rate is proportional to the difference between the maximum potential for learning, M, and the amount of the skill already learned, L. This means that as L increases, the difference (M - L) decreases, and so does the learning rate. Proportionality in this context suggests a direct relationship between the rate of change of L and (M - L).Deriving the Relationship: The rate of change of a quantity is represented by its derivative with respect to time. Therefore, the rate of change of L with respect to time, t, is written as (dL)/(dt). Since the learning rate is proportional to (M - L), we can express this relationship with a constant of proportionality, k.Mathematical Representation: The correct mathematical representation of this relationship is (dL)/(dt) = k(M - L), where k is the constant of proportionality. This equation shows that the rate at which L changes with time is equal to k times the difference between M and L.Matching the Options: Looking at the given options, we can see that option (C) (dL)/(dt) = k(M - L) matches our derived relationship. Therefore, this is the correct equation that describes the given relationship.

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