Answered: In a nursery, the reason for spreading…

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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Question

In a nursery, the reason for spreading a virus epidemic is equal to half of those who have not gotten sick yet. if 200 children are enrolled in the nursery, give a differential equation for the number of children infected N with respect to time t in days.

Solve the differential equation to answer the following: If a sick child started the epidemic, will they all be infected three days later?

Expert Solution

Step 1

Number of children infected N w.r.t to time t in days

$\frac{d N}{d t} = N$

Use variable saprable method to solve differential equation

$\int \frac{d ℕ}{N} = \int d t$

LogN =t +c

N =100 at t =0

log100 = c

c=2

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