Thank you for the opportunity to help you with your question!
a) it is N(x=0) = 8000/(200) = 40
b) the rate is
dN/dx = 8000*(-1)*(-199*e^(-x))/(1+199e^(-x))^2 = 8000*199e^(-x)/(1+199*e^(-x))^2 >0
thus N(x) is increases in (0, infinity).
hi can you clarify what the answer to b is
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