Students in a psychology class look a final examination. As part of an experiment to see how much of the course content they remembered over time, they took equivalent forms of the exam in monthly intervals thereafter. The average score, f ( t ) , for the group after t months is modeled by the function f ( t ) = 76 − 18 log ( t + 1 ) , where 0 ≤ t ≤ , 12 . a. What was the average score when the exam was first given? b. What was the average score after 2 months? 4 months? 6 months? 8 months? one year? c. Use the results from parts (a) and (b) to graph f. Describe what the shape of the graph indicates in terms of the material retained by the students.
Students in a psychology class look a final examination. As part of an experiment to see how much of the course content they remembered over time, they took equivalent forms of the exam in monthly intervals thereafter. The average score, f ( t ) , for the group after t months is modeled by the function f ( t ) = 76 − 18 log ( t + 1 ) , where 0 ≤ t ≤ , 12 . a. What was the average score when the exam was first given? b. What was the average score after 2 months? 4 months? 6 months? 8 months? one year? c. Use the results from parts (a) and (b) to graph f. Describe what the shape of the graph indicates in terms of the material retained by the students.
Solution Summary: The author calculates the average score for the group after t months using the function f(t)=76-18mathrm
Students in a psychology class look a final examination. As part of an experiment to see how much of the course content they remembered over time, they took equivalent forms of the exam in monthly intervals thereafter. The average score,
f
(
t
)
, for the group after t months is modeled by the function
f
(
t
)
=
76
−
18
log
(
t
+
1
)
, where
0
≤
t
≤
,
12
.
a. What was the average score when the exam was first given?
b. What was the average score after 2 months? 4 months? 6 months? 8 months? one year?
c. Use the results from parts (a) and (b) to graph f. Describe what the shape of the graph indicates in terms of the material retained by the students.
4. Use method of separation of variable to solve the following wave equation
მłu
J²u
subject to
u(0,t) =0, for t> 0,
u(л,t) = 0, for t> 0,
=
t> 0,
at²
ax²'
u(x, 0) = 0,
0.01 x,
ut(x, 0) =
Π
0.01 (π-x),
0
Solve the following heat equation by method of separation variables:
ди
=
at
subject to
u(0,t) =0, for
-16024
ძx2 •
t>0, 0 0,
ux (4,t) = 0, for
t> 0,
u(x, 0) =
(x-3,
\-1,
0 < x ≤2
2≤ x ≤ 4.
ex
5.
important aspects.
Graph f(x)=lnx. Be sure to make your graph big enough to easily read (use the space given.) Label all
6
33
Chapter 3 Solutions
Precalculus, Books A La Carte Edition Plus MyLab Math with eText -- Access Card Package (6th Edition)
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