(P2) Suppose two students are memorizing the elements on a list according to the rate of change equation: dL/dt = 0.5(1-L). L represents the fraction of the list that is memorized at any time t. (c) Suppose now that the list is infinitely long, like the decimal representation for π. In reality no one can memorize all the digits to π, but what does the rate of change equation predict will happen for a person who starts out not knowing any of the digits? That is, according to the rate of change equation, if L = 0 at time t = 0, is there ever a value of t for which L = 1? Explain.
(P2) Suppose two students are memorizing the elements on a list according to the rate of change equation: dL/dt = 0.5(1-L). L represents the fraction of the list that is memorized at any time t.
(c) Suppose now that the list is infinitely long, like the decimal representation for π. In reality no one can memorize all the digits to π, but what does the rate of change equation predict will happen for a person who starts out not knowing any of the digits? That is, according to the rate of change equation, if L = 0 at time t = 0, is there ever a value of t for which L = 1? Explain.
Given that the rate of learning is,
Where L represents the fraction of list that is memorized at any time .
For a person starting with no prior knowledge of digits of π, starts at learning rate,
As he keeps on learning more digits this rate slows down as L increases.
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