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) (dL)/(dt)=k(M-L) (C) L(t)=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)  (dL)/(dt)=k(M-L) (C)  L(t)=k(M-L) (D)  (dL)/(dt)=(k)/((M-L))

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Identify Relationship Equation: The problem states that the learning rate is proportional to the difference between the maximum potential, M, and the amount already learned, L. This suggests that the rate of change of L with respect to time, (dL)/(dt), is directly proportional to (M - L). We need to find an equation that represents this relationship.Eliminate Incorrect Options: Looking at the options, we can eliminate (A) and (C) because they do not represent a rate of change over time; they are expressions for L(t) without any differentiation. We are looking for an equation that involves (dL)/(dt), which is the derivative of L with respect to time, indicating a rate of change.Select Correct Option: Option (B) states that (dL)/(dt) = k(M - L), which aligns with the description given in the problem. It shows that the rate of change of L with respect to time is proportional to the difference (M - L), with k being the constant of proportionality.Analyze Option D: Option (D) suggests that (dL)/(dt) is equal to k divided by (M - L), which would imply that the learning rate decreases as the difference (M - L) increases. This is contrary to the problem statement, which says the learning rate is directly proportional to (M - L), not inversely proportional.

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