Graphs of Exponential Functions

[nycmathguy]

Section 3.1

The graph of g(x) = 4^x appears to be steeper than the graph of f(x) = 2^x. Any particular reason for this change in terms of steepness? I guess what I'm trying to say is that the graph of g(x) increases faster than the graph of f(x). Why?

 

[MathLover1]

Exponential Function
ƒ(x) = b^x
The larger the base b, the stepper/faster the increase.

 

[nycmathguy]

Exponential Function
ƒ(x) = b^x
The larger the base b, the stepper/faster the increase.

Say we have two exponential functions:

g(x) = 7^(x) and h(x) = 14^(x).

You are saying that h(x) is steeper and faster as it increases because 14 > 7.

Yes?

However, both functions increase without bound.

Yes?

 

[MathLover1]

yes

 

[nycmathguy]

yes

Very good. I truly hope not to be bombarding you with too many math questions. In fact, how many questions is enough for you per day?