Austin is using graphs to compare the growth rates of g(x)=1.3x and f(x)=1.3x

Question

. 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)=1.3x
is only greater than the growth rate of f(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)=1.3x
is only greater than the growth rate of g(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 f(x)=1.3x
will quickly surpass the growth rate of g(x)=1.3x
Austin should compare the steepness of the curves. The growth rate of f of x is equal to 1 point 3 to the x th power will quickly surpass the growth rate of g of x is equal to 1 point 3 x

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

The functions \( g(x) = 1.3^x \) and \( f(x) = 1.3^x \) are actually the same functions; therefore, their growth rates are identical at all points. Thus, comparing their growth rates will show that they are equal, which doesn't align with any responses that imply one grows faster than the other after a certain point.

The correct answer from the provided options is:

Austin should compare the steepness of the curves. The growth rate of \( f(x) = 1.3^x \) is equal to the growth rate of \( g(x) = 1.3^x \).

However, since this particular answer is not provided among the options, the closest fitting response is:

Austin should find where one curve is above the other curve on the graph. The growth rate of \( f(x)=1.3^x \) is equal to the growth rate of \( g(x)=1.3^x \) at all points.

If there’s no option that states the right insight (that they are equal everywhere), you might select an option related to comparing steepness and that they grow at the same rate.