Which of the following functions grows the fastest as x goes to infinity?

Question

3^x
ln(x)
e^4x
x^10

I put e^4x but I thought that 3^x might have been it too. I know for sure that it is not ln(x) and x^10 because those grow much slower.

Answer 1

yes, e^(4x) grows at the fastest rate

e.g. let x = 20, (not very large at all)

3^20 = 3.48 x 10^9
ln(20) = only about 3
e^(4x) = 5.5 x 10^34 <------
20^10 = 1.024 x 10^13