Austin is using graphs to compare the growth rates of g(x)=1.3x and f(x)=1.3xg(x)=1.3x and f(x)=1.3x . Which statement correctly describes how Austin should do this and what he will observe?(1 point) Responses Austin should find where one curve is above the other curve on the graph. The growth rate of g(x)=1.3xg(x)=1.3x is only greater than the growth rate of f(x)=1.3xf(x)=1.3x to the right of their right-most intersection point. Austin should find where one curve is above the other curve on the graph. The growth rate of g of x is equal to 1 point 3 x is only greater than the growth rate of f of x is equal to 1 point 3 to the x th power to the right of their right-most intersection point. Austin should find where one curve is above the other curve on the graph. The growth rate of f(x)=1.3xf(x)=1.3x is only greater than the growth rate of g(x)=1.3xg(x)=1.3x to the right of their right-most intersection point. Austin should find where one curve is above the other curve on the graph. The growth rate of f of x is equal to 1 point 3 to the x th power is only greater than the growth rate of g of x is equal to 1 point 3 x to the right of their right-most intersection point. Austin should compare the steepness of the curves. The growth rate of g(x)=1.3xg(x)=1.3x will quickly surpass the growth rate of f(x)=1.3xf(x)=1.3xAustin should compare the steepness of the curves. The growth rate of g of x is equal to 1 point 3 x will quickly surpass the growth rate of f of x is equal to 1 point 3 to the x th power Austin should compare the steepness of the curves. The growth rate of f(x)=1.3xf(x)=1.3x will quickly surpass the growth rate of g(x)=1.3x

Answer 1

To compare the growth rates of the functions \( g(x) = 1.3^x \) and \( f(x) = 1.3x \), Austin should analyze the curves on a graph.

The correct statement is:

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 \( g(x) = 1.3^x \) to the right of their right-most intersection point.

Explanation:

1. Growth Rates: \( g(x) = 1.3^x \) is an exponential function, which generally increases faster than \( f(x) = 1.3x \), a linear function, as \( x \) becomes large.
2. Intersections: At some points, particularly at small values of \( x \), \( f(x) \) may be greater than \( g(x) \). However, beyond a certain point, \( g(x) \) will exceed \( f(x) \) and continue to grow at a faster rate.
3. Conclusion: Thus, the intersection point indicates where the growth rates will change in relation to each other. Beyond this point, \( g(x) \) will be greater than \( f(x) \).