The 2003 SARS Outbreak In the early stages of the SARS (severe acute respiratory syndrome) epidemic in 2003, the number of reported cases could be approximated by A ( t ) = 167 ( 1.18 ) t ( 0 ≤ t ≤ 20 ) t days after March 17,2003 (the first day in which statistics were reported by the World Health Organization.) a. What, approximately, was the instantaneous rate of change of A ( t ) on March 27 ( t = 10 ) ? Interpret the result. b. Which of the following is true? For the first 20 days of the epidemic, the instantaneous rate of change of the number of cases (A) increased. (B) decreased. (C) increased and then decreased. (D) decreased and then increased.
The 2003 SARS Outbreak In the early stages of the SARS (severe acute respiratory syndrome) epidemic in 2003, the number of reported cases could be approximated by A ( t ) = 167 ( 1.18 ) t ( 0 ≤ t ≤ 20 ) t days after March 17,2003 (the first day in which statistics were reported by the World Health Organization.) a. What, approximately, was the instantaneous rate of change of A ( t ) on March 27 ( t = 10 ) ? Interpret the result. b. Which of the following is true? For the first 20 days of the epidemic, the instantaneous rate of change of the number of cases (A) increased. (B) decreased. (C) increased and then decreased. (D) decreased and then increased.
Solution Summary: The author calculates the instantaneous rate of change of the number of cases reported on March 27 using the balance difference quotient.
The 2003 SARS Outbreak In the early stages of the SARS (severe acute respiratory syndrome) epidemic in 2003, the number of reported cases could be approximated by
A
(
t
)
=
167
(
1.18
)
t
(
0
≤
t
≤
20
)
t days after March 17,2003 (the first day in which statistics were reported by the World Health Organization.)
a. What, approximately, was the instantaneous rate of change of
A
(
t
)
on March
27
(
t
=
10
)
? Interpret the result.
b. Which of the following is true? For the first 20 days of the epidemic, the instantaneous rate of change of the number of cases
2. (5 points) Let f(x) =
=
-
-
- x² − 3x+7. Find the local minimum and maximum point(s)
of f(x), and write them in the form (a, b), specifying whether each point is a minimum
or maximum. Coordinates should be kept in fractions.
Additionally, provide in your answer if f(x) has an absolute minimum or maximum
over its entire domain with their corresponding values. Otherwise, state that there is no
absolute maximum or minimum. As a reminder, ∞ and -∞ are not considered absolute
maxima and minima respectively.
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