Question 1042169
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a) 



The initial count n happens when x = 0.



Plug in x = 0 to get:



{{{n=15000/(1+999e^(-0.8x))}}}



{{{n=15000/(1+999e^(-0.8*0))}}}



{{{n=15000/(1+999e^(0))}}}



{{{n=15000/(1+999*1)}}}



{{{n=15000/(1+999)}}}



{{{n=15000/(1000)}}}



{{{n=15}}}



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 {{{999e^(-0.8x)}}} gets smaller.



Using limits, as x approaches infinity,  {{{999e^(-0.8x)}}} approaches 0.



So effectively {{{n=15000/(1+999e^(-0.8x))}}} turns into {{{n=15000/(1+0)}}} when x gets very very large. 



That simplifies to {{{n = 15000}}} 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. 
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