Find the lim t -> infinity of: 1/(1 + ae^(-kt))

[MarkSA]

Hello,

Under certain circumstances, a rumor spreads according to the equation:
p(t) = 1/(1 + ae^(-kt))
where p(t) is the proportion of the population that knows the rumor at time 't' and 'a' and 'k' are positive constants.

Find the lim as t -> infinity of p(t).

I'm a little unsure where to begin on this. I've always been a little fuzzy on evaluating limits that go to infinity. In the past, I think i've done it by eyeing the problem more than anything? But, i'm not sure how to do that with the ae^(-kt) mess.

 

[Deleted member 4993]

what is the value of

e^(-kt) = 1/[e^(kt)] as t goes to very large number (infinity)?

 

[MarkSA]

Ok, thanks.. I see how it approaches 1 now. That was the answer the book had too I believe.

Is there an some other written way of showing work on limits to infinity though? Or is it just a matter of eyeing it or breaking it up so that each piece can be evaluated as it goes to infinity?