Compare the two functions in the table. Will the value of function y = 2x eventually exceed the value of function y = x10?

First we rewrite the functions:

y = 2x

y = x ^ 10

We note that the second function always has values of y greater than the first function. However, there is a value of x for which the first function is greater.

For x = 1 we have:

y = 2 (1) = 2

y = (1) ^ 10 = 1

We note that:

2> 1

Answer:

Yes, the value of function y = 2x eventually exceed the value of function y = x ^ 10.