Laplace Growth restriction

1. Dec 21, 2008

KateyLou

1. The problem statement, all variables and given/known data
The condition to be satisfied for a Laplace transform is U(t)<Mekt

2. Relevant equations
I am trying to proove that et2 does not satisfy this

3. The attempt at a solution
It was suggested that we try taking logarithms of both side:
t2<ln(Mekt)
t2<lnM+lnekt
t2<lnM+kt
t2-kt<ln M

I dont think this shows anything?!

2. Dec 21, 2008

Dick

Sure it shows something. t^2-kt is unbounded as t->infinity. ln(M) is a constant. t^2-kt<ln(M) can't be true for all t.

3. Dec 21, 2008

KateyLou

YAY! Thank you!