Results of studying. Celia’s score on a test, s ( t ) , after t hours of studying, is given by s ( t ) = t 2 , 0 ≤ t ≤ 10 , Dan’s score on the same test is given by S ( t ) = 10 t , 0 ≤ t ≤ 10 , where S ( t ) is his score after t hours of studying. a. For 0 < t < 10 , who will have the higher test score? b. Find the average value of s ( t ) over [ 7 , 10 ] , and explain what it represents. c. Find the average value of S ( t ) over [ 6 , 10 ] , and explain what it represents. d. Assuming that both students have the same study habits and are equally likely to study for any number of hours, t, in [0, 10][0, 10], on average, how far apart will their test scores be?
Results of studying. Celia’s score on a test, s ( t ) , after t hours of studying, is given by s ( t ) = t 2 , 0 ≤ t ≤ 10 , Dan’s score on the same test is given by S ( t ) = 10 t , 0 ≤ t ≤ 10 , where S ( t ) is his score after t hours of studying. a. For 0 < t < 10 , who will have the higher test score? b. Find the average value of s ( t ) over [ 7 , 10 ] , and explain what it represents. c. Find the average value of S ( t ) over [ 6 , 10 ] , and explain what it represents. d. Assuming that both students have the same study habits and are equally likely to study for any number of hours, t, in [0, 10][0, 10], on average, how far apart will their test scores be?
Solution Summary: The author explains the formula for the natural logarithm rule: the score of Celina is the integral of the function s(t) in the interval
Results of studying. Celia’s score on a test,
s
(
t
)
, after t hours of studying, is given by
s
(
t
)
=
t
2
,
0
≤
t
≤
10
,
Dan’s score on the same test is given by
S
(
t
)
=
10
t
,
0
≤
t
≤
10
,
where
S
(
t
)
is his score after t hours of studying.
a. For
0
<
t
<
10
, who will have the higher test score?
b. Find the average value of
s
(
t
)
over
[
7
,
10
]
, and explain what it represents.
c. Find the average value of
S
(
t
)
over
[
6
,
10
]
, and explain what it represents.
d. Assuming that both students have the same study habits and are equally likely to study for any number of hours, t, in [0, 10][0, 10], on average, how far apart will their test scores be?
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Fundamental Theorem of Calculus 1 | Geometric Idea + Chain Rule Example; Author: Dr. Trefor Bazett;https://www.youtube.com/watch?v=hAfpl8jLFOs;License: Standard YouTube License, CC-BY