The function with the greatest rate of change as x approaches infinity is f(x) = 2^x - 10
Which function has the greatest rate?
To check this, we need to differentiate the given functions. We will have:
Now, we want to see which function has the greatest rate of change for large values of x (ax x approaches to infinity).
So we can just evaluate these for a large value of x, let's say, 10, and see which one gives the largest value:
- f'(10) = 2^10 = 1,024
- g'(10) = 16
- h'(10) = 53
Already with this, we can conclude that the function with the greatest rate of change as x approaches infinity is the one in option A. This is a tendency we will see in math, exponential functions always grow faster than other functions for larger values of x.
If you want to learn more about rates of change, you can read:
https://brainly.com/question/8728504
