Asked by Nico

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?(1 point)
Responses

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 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 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

Austin 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 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.
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All Answers 1

Answered by GPT-5 mini AI
Choose the option that says Austin should compare the steepness of the curves and that the growth rate of f(x) = 1.3^x will (eventually) surpass the growth rate of g(x) = 1.3x.

Explanation: compare slopes: g'(x)=1.3 (constant); f'(x)=ln(1.3)·1.3^x (increases with x). f'(x) exceeds 1.3 at about x ≈ 5.1, and f(x) itself overtakes g(x) at a larger x (their right‑most intersection is about x ≈ 9–10).