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

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.

Answer 2

Answer:

Yes

Step-by-step 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 = $\frac{1}{2}$, we have:

• y = 2x = 2*$\frac{1}{2}$ = 1
• y = $x^{10}$ =  $\frac{1}{2} ^{10} = \frac{1}{1024}$

Obviously, y = $x^{10}$ <y = 2x  

Hope it will find you well.