CS brainlet here, why e^x grows so much faster than 2^x? 2.7182818284 is not much bigger than 2.0?
Here is code in python:
for i in range(0,10000):
print(i, " : ", math.exp(i))
for i in range(0,10000):
print(i, " : ", 2**i)
First loop overflows on i~=800. Second loop does not overflows.