Ebbinghaus learning model. Suppose that you are given the task of learning 100% of knowledge. Human nature is such that we retain only a percentage P of knowledge t weeks after we have learned it. The Ebbinghaus learning model asserts that P is given by P ( t ) = Q + ( 100 − Q ) e − k t , where Q is the percentage that we would never forget and k is a constant that depends on the knowledge learned. Suppose that Q = 40 and k = 0.7 . a. Find the percentage retained after 0 weeks, 1 week, 2 weeks, 6 weeks, and 10 weeks. b. Find lim t → ∞ P ( t ) . 40 % c. Sketch a graph of P . d. Find the rate of change of P ( t ) with respect to time t . e. Interpret the meaning of the derivative.
Ebbinghaus learning model. Suppose that you are given the task of learning 100% of knowledge. Human nature is such that we retain only a percentage P of knowledge t weeks after we have learned it. The Ebbinghaus learning model asserts that P is given by P ( t ) = Q + ( 100 − Q ) e − k t , where Q is the percentage that we would never forget and k is a constant that depends on the knowledge learned. Suppose that Q = 40 and k = 0.7 . a. Find the percentage retained after 0 weeks, 1 week, 2 weeks, 6 weeks, and 10 weeks. b. Find lim t → ∞ P ( t ) . 40 % c. Sketch a graph of P . d. Find the rate of change of P ( t ) with respect to time t . e. Interpret the meaning of the derivative.
Solution Summary: The author calculates the percentage of retained knowledge of task after 0week, 1 - 2 weeks.
Ebbinghaus learning model. Suppose that you are given the task of learning 100% of knowledge. Human nature is such that we retain only a percentage P of knowledge t weeks after we have learned it. The Ebbinghaus learning model asserts that P is given by
P
(
t
)
=
Q
+
(
100
−
Q
)
e
−
k
t
,
where Q is the percentage that we would never forget and k is a constant that depends on the knowledge learned. Suppose that
Q
=
40
and
k
=
0.7
.
a. Find the percentage retained after 0 weeks, 1 week, 2 weeks, 6 weeks, and 10 weeks.
b. Find
lim
t
→
∞
P
(
t
)
.
40
%
c. Sketch a graph of P.
d. Find the rate of change of
P
(
t
)
with respect to time t.
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