Question

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

Answer 1

Yes

Explanation:

Allow me to revise your question for a better understanding

y = 2x

y =
`x^(10)`

Any exponential function with a base bigger than 0 smaller than 1 will eventually be exceeded by any polynomial function. Let me give one example for this situation.

Let x =
`(1)/(2)`, we have:

• y = 2x = 2*
  `(1)/(2)` = 1
• y =
  `x^(10)` =
  `(1)/(2) ^(10) = (1)/(1024)`

Obviously, y =
`x^(10)` <y = 2x

Hope it will find you well.

Answer 2

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.