Austin is using graphs to compare the growth rates of g(x) = 1.3x and f(x) = 1.3x. Which statement correctly describes how Austin should do this and what he will observe?

Question

A) Austin should find where one curve is above the other curve on the graph. The growth rate of g(x) = 1.3x is only greater than the growth rate of f(x) = 1.3x.
B) Austin should compare the steepness of the curves. The growth rate of f(x) = 1.3x will quickly surpass the growth rate of g(x) = 1.3x
C) Austin should find where one curve is above the other curve on the graph. The growth rate of f(x) = 1.3x is only greater than the growth rate of g(x)=1.3x to the right of their right-most intersection point.
D) Austin should compare the steepness of the curves. The growth rate of g(x) = 1.3x will quickly surpass the growth rate of f(x) = 1.3x

Answer 1

To compare the functions \( g(x) = 1.3^x \) and \( f(x) = 1.3^x \), we need to clarify a potential misunderstanding in the provided choices.

Both functions are actually the same, \( g(x) = f(x) \). Therefore, their growth rates are identical, and there is no point at which one curve is above the other or where one surpasses the other.

With that in mind, the correct choice among the statements provided is:

None of the given options accurately describe the situation, as all of them imply a difference in growth rates between the two functions, which is not the case. Both functions exhibit the same growth rate because they are equal.

If you'd like to modify or clarify the functions or options for better analysis, please let me know!