Question

Which function increases at a faster rate on 0 to infinity, f(x)=x^2 or g(x)=2^x?Explain your reasoning.

Answer 1

look at the picture

Explanation:

edge

Answer 2

g(x) increase at a faster rate.

Explanation:

Given : Two functions
`f(x)=x^2` or
`g(x)=2^x`

To find : Which function increase at a faster rate on 0 to infinity

Solution :

We put some value of x in the functions and note down the observation.

x → 0 1 2 3 4 5 6 7

`f(x)=x^2` → 0 1 4 9 16 25 36 49

`g(x)=2^x` → 1 2 4 8 16 32 64 128

Comparing the values of f(x) and g(x), we can see that that g(x) increases at a faster rate on 0 to infinity.

Reason - The exponential function, g(x), has a constant multiplicative rate of change and will increase at a faster rate than the quadratic function f(x).