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
3. Consider the initial value problem
9y" +12y' + 4y = 0, y(0) = a>0: y′(0) = −1.
Solve the problem and find the value of a such that the solution of the initial value problem is always
positive.
5. Euler's equation.
Determine the values of a for which all solutions of the equation
5
x²y" + axy' + y = 0
that have the form (A + B log x) x* or Ax¹¹ + Bä” tend to zero as a approaches 0.
4. Problem on variable change.
The purpose of this problem is to perform an appropriate change of variables in order to reduce
the problem to a second-order equation with constant coefficients.
ty" + (t² − 1)y'′ + t³y = 0, 0
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