The number of cases of influenza in New York City from the beginning of 1960 to the beginning of 1964 is modeled by the functionN(t) = 5.3e0.093r? -0.871 .for 0

Answered: The number of cases of influenza in New…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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The number of cases of influenza in New York City from the beginning of 1960 to the beginning of 1964 is modeled by the function
N(t) = 5.3e0.093r? -0.871 .
for 0 <t<4
where N(t) gives the number of cases (in thousands) and t is measured in years, with t= 0 corresponding to the beginning of 1960.
(a)
] Give N(0) and N(3). Briefly describe what these values indicate about the disease in New York City.
(b) [!
Give the formula for evaluating N' (t).
(c)
s) Find N'(0) and N'(2). Briefly describe what these values indicate about the disease in New York City during this timeframe.
Hints:
(1) It may be helpful to check out Section 3.4 in your text.
ΔΝ
(2) The derivative N'(t) is approximately equal to
At
where
AN = N(t+ h) – N(t)
and
At = (t + h) – t.
and h is small (h 0
You should use this idea in your descriptions.

Expert Solution

Step 1

$G i v e n, N (t) = 5.3 e^{0.093 t^{2} - 0.87 t} (a) N (0) = 5.3 e^{0.093 {(0)}^{2} - 0.87 (0)} = 5.3 e^{0} = 5.3 N (3) = 5.3 e^{0.093 {(3)}^{2} - 0.87 (3)} = 5.3 e^{- 1.773} = 0.90006 A s t h e n u m b e r o f y e a r s i n c r e a s e s, t h e n u m b e r o f c a s e s o f i n f l u e n z a i n N e w Y o r k c i t y d e c r e a s e s .$

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