Answer:
Option C.
Step-by-step explanation:
We know that, for a value a > 1.
if b > c, then:
a^b > a^c
Now, this means that if we have two functions:
f(x) = x^n
g(x) = x^m
and m > n
then for large values of x, g(x) will be larger than f(x), because g(x) has a larger exponent.
now, is also true that:
f(x) = x^n
g(x) = n^x
for n > 1
For large values of x, g(x) will be larger than f(x), again, because for larger values of x g(x) will have a really large exponent, thus it grows really fast.
Then we can conclude that for the functions:
f(x) = 3*x
g(x) = 3*x^2
h(x) = 2^x
For a given value of x, h(x) will exceed the other two functions.
This can be seen in the graph below, where:
h(x) is purple, g(x) is blue, and f(x) is green.
We can see that eventually, h(x) exceeds the other two.
The correct option is C.
