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

g(x) increase at a faster rate.

Step-by-step explanation:

Given : Two functions   or

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      

 →  0      1       4      9      16       25       36      49

→   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).  

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step-by-step explanation: