There's a school of 1000 fish, the number P infected with a disease at time t years is given by P = #1000/(1+ce^-(1000t)# where c is a constant. How do you show that eventually all the fish will become infested?

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Answer 1 · 2017-12-24T09:23:35

See below.

#P=1000/(1+ce^-(1000t)#

#e^-(1000t)=1/e^(1000t)#

#:.#

#lim_(t->oo)(1/e^(1000t))=0#

#:.#

#lim_(t->oo)(1000/(1+ce^-(1000t)))=1000/(1+0)=1000=P#

This is true for any constant #c#