April 21st question
Assume that a certain network can be approximated by a particular continuous model, and its number of nodes increases at a rate given by the function \( f(t) = e^{\frac{-t}{1000}+10} \).
Given that at \( t=0 \), the number of nodes is 0, what is the approximate maximum number of nodes that this network can have? Tip: get an expression for the number of nodes \( N(t) \) and its limit when \( t \rightarrow \infty \).
- \( e^{\frac{-1}{3}+10} \).
- \( 1000\ e^{\frac{-1}{3}+10} \).
- \( 1000\ e^{10} \).
- \( e^{10} \).
- None of the above
Original idea by: Christian Konishi
Something is wrong with this question. According to the formula, when t = 0 the number of nodes is e¹⁰, not 0.
ResponderExcluirf(0) is indeed e^{10}, but f is not the number of nodes, it is the rate that they increase. The idea is that I can get an expression for the number of nodes by integrating it and applying the condition N(0) = 0
Excluir