Consider a setting where subjects have a list of M words to memorize. We wish to mathematically model the memory retention of these words. One simple theory is that the rate of change of the number of words memorized is proportional to how many words there are left to be memorized. To account for the possibility of forgetting words, the theory also suggests that words are forgotten at a rate proportional to the amount of words already memorized. In general, the constants of proportionality are different for memorizing and forgetting. (a) Define the variables and parameters involved and represent each with a letter to be used in the model. (b) Write a differential equation model based on this description and your choices in part 1a. ( c) Find the equilibrium point(s) of the model you came up with in part 1b. (d) Determine the stability of each equilibrium point. (e) What do your results from part 1d tell you about how many words someone will retain in the long run according to this model? No hand written solution and no image
Consider a setting where subjects have a list of M words to memorize. We wish to mathematically model the memory retention of these words. One simple theory is that the rate of change of the number of words memorized is proportional to how many words there are left to be memorized. To account for the possibility of forgetting words, the theory also suggests that words are forgotten at a rate proportional to the amount of words already memorized. In general, the constants of proportionality are different for memorizing and forgetting.
(a) Define the variables and parameters involved and represent each with a letter to be used in the model.
(b) Write a
c) Find the equilibrium point(s) of the model you came up with in part 1b.
(d) Determine the stability of each equilibrium point.
(e) What do your results from part 1d tell you about how many words someone will retain in the long run according to this model? No hand written solution and no image
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