On a college campus of 5,000 students, one student returns from vacation with a contagious flu virus. The spread of the virus is modeled by:y=5000/(1+4999e-0.8t)t is greater than or equal to 0Where y is the total number infected after t days. The college will cancel classes when 40% or more of the students are infected.After how many days will the college cancel classes?

Question
Asked Nov 25, 2019
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On a college campus of 5,000 students, one student returns from vacation with a contagious flu virus. The spread of the virus is modeled by:

y=5000/(1+4999e-0.8t)

t is greater than or equal to 0

Where y is the total number infected after t days. The college will cancel classes when 40% or more of the students are infected.

After how many days will the college cancel classes?

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Expert Answer

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Step 1

Given:

Total students in the campus is 5000.
5000
...1), 120
y =
1+4999e0.8r
Where y is the total number students infected after t days.
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Total students in the campus is 5000. 5000 ...1), 120 y = 1+4999e0.8r Where y is the total number students infected after t days.

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Step 2

Calculation:

It is given that, the college will cancel classes when 40% or more of the students are infected
So that, 40% of 5000 is,
40
x 5000 = 2000
100
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It is given that, the college will cancel classes when 40% or more of the students are infected So that, 40% of 5000 is, 40 x 5000 = 2000 100

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Step 3
From (1)
5000
2000
1+4999e
5000
1+4999e8
2000
1+4999e.8 2.5
4999e
4999e
0.8t
= 2.5-1
0.8
=1.5
1.5
-0.8f
4999
= (0.0003)
0.8t
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From (1) 5000 2000 1+4999e 5000 1+4999e8 2000 1+4999e.8 2.5 4999e 4999e 0.8t = 2.5-1 0.8 =1.5 1.5 -0.8f 4999 = (0.0003) 0.8t

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