SOLUTION: A Contagious disease enters a college campus, and the number of students infected by the disease is given by n=15000/(1+999e^(-0.8x)) where x is the number of days after the diseas

Question 1042169: A Contagious disease enters a college campus, and the number of students infected by the disease is given by n=15000/(1+999e^(-0.8x)) where x is the number of days after the disease appears on a campus.
a.) How many students had the disease when it appeared on campus?
b.) What is the upper limit of the number of students infected by the disease?
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

a)

The initial count n happens when x = 0.

Plug in x = 0 to get:

So 15 students had the disease when it appeared on campus.

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b)

Notice how as x gets larger and larger, the expression gets smaller.

Using limits, as x approaches infinity, approaches 0.

So effectively turns into when x gets very very large.

That simplifies to which is the limiting value. This is the upper ceiling so to speak of all the number of people who can get infected. The value of n won't actually reach 15000 but it will get closer and closer.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A Contagious disease enters a college campus, and the number of students infected by the disease is given by N(x) = 15000/(1+999^-0.8e^x) where x is the number of days after the disease appears on a campus.
a.) How many students had the disease when it appeared on campus?
N(0) = (15000/(1+999^0) = 15000/1000 = 15
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b.) What is the upper limit of the number of students infected by the disease?
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As x increases, 999^-0.8e^x approaches zero.
Ans:: upper limit = 15000/1 = 15000
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Cheers,
Stan H.
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