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

Answer:g(x) increase at a faster rate.Step-by-step explanation:Given : Two functions  [tex]f(x)=x^2[/tex] or [tex]g(x)=2^x[/tex]To find : Which function increase at a faster rate on 0 to infinitySolution :We put some value of x in the functions and note down the observation.             x               →  0      1      2       3       4        5        6         7      [tex]f(x)=x^2[/tex]  →  0      1       4      9      16       25       36      49 [tex]g(x)=2^x[/tex] →   1      2      4       8      16        32      64      128Comparing 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).