Math Is Fun Forum

willis

Member

Registered: 2010-02-24

Posts: 7

Virus spread

The spread of a virus through a city is modeled by the function

N = 15000/( 1 + 100e -0.5t)

When N is the number of people infected by the virus after t days. How many days it takes for 2000 people of this city to be infected with the virus.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Virus spread

Substitute 2000 for the N in your equation, and then solve for t.

2000  = 15000/(1 + 100e^(-0.5t))
But 2000 = 15000/7.5, so (1 + 100e^(-0.5t)) = 7.5

Therefore 100e^(-0.5t) = 6.5, and so e^(-0.5t) = 0.065.
Taking logs, -0.5t = -2.733...
And so, t = 5.467, to three decimal places.

In other words, a little over 5 days, 11 hours.

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Why did the vector cross the road?
It wanted to be normal.