When the forgetfulness of an individual is taken into account, the speed with which he memorizes is defined by dA/dt = k1 (M − A) − k2A, in what k1 > 0, k2 > 0, A(t) is the amount of material memorized at time t, M is the total amount to memorize and M − A is the amount remaining to memorize. Find A(t) and graph the solution. Suppose A(0) = 0. Determine the limit value of A when t → ∞ e. interpret the result.
When the forgetfulness of an individual is taken into account, the speed with which he memorizes is defined by dA/dt = k1 (M − A) − k2A, in what k1 > 0, k2 > 0, A(t) is the amount of material memorized at time t, M is the total amount to memorize and M − A is the amount remaining to memorize. Find A(t) and graph the solution. Suppose A(0) = 0. Determine the limit value of A when t → ∞ e. interpret the result.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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When the forgetfulness of an individual is taken into account, the speed with which he memorizes is
defined by
dA/dt = k1 (M − A) − k2A, in what k1 > 0, k2 > 0, A(t)
is the amount of material memorized at time t, M is the total amount to memorize and M − A is the amount remaining to memorize. Find A(t) and
graph the solution. Suppose A(0) = 0. Determine the limit value of A when t → ∞ e. interpret the result.
topic: ORDINARY DIFFERENTIAL EQUATIONS
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