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

All exponential function s with run at a faster rate then quadratics
g(x) is thus going at a faster rate

Answer 2

Answer:

g(x) increase at a faster rate.

Step-by-step 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).