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

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> 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      Log On


   

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) About Me  (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:


n=15000%2F%281%2B999e%5E%28-0.8x%29%29


n=15000%2F%281%2B999e%5E%28-0.8%2A0%29%29


n=15000%2F%281%2B999e%5E%280%29%29


n=15000%2F%281%2B999%2A1%29


n=15000%2F%281%2B999%29


n=15000%2F%281000%29


n=15


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


--------------------------------------------------


b)


Notice how as x gets larger and larger, the expression 999e%5E%28-0.8x%29 gets smaller.


Using limits, as x approaches infinity, 999e%5E%28-0.8x%29 approaches 0.


So effectively n=15000%2F%281%2B999e%5E%28-0.8x%29%29 turns into n=15000%2F%281%2B0%29 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.

Answer by stanbon(75887) About Me  (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
----------------------------------------------------
b.) What is the upper limit of the number of students infected by the disease?
--------------------------------
As x increases, 999^-0.8e^x approaches zero.
Ans:: upper limit = 15000/1 = 15000
---------------
Cheers,
Stan H.
--------------------