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 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
[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 64 128
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).
