Question

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 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 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 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.

Answer 1

Choose the option that says Austin should compare the steepness of the curves and that f(x) = 1.3^x will (eventually / quickly) surpass the growth of g(x) = 1.3x.

Reason: g(x)=1.3x is linear with constant slope 1.3, while f(x)=1.3^x is exponential with increasing slope. For large x the exponential's slope and values grow faster than the linear.