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 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 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
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.

Answer 1

To accurately evaluate the comparison of the growth rates of \( g(x) = 1.3^x \) and \( f(x) = 1.3^x \) (which are actually the same function), Austin should look at the functions and their properties directly.

Since both functions are identical, they will always have the same value for any given \( x \). Therefore, their curves will be on top of each other for all \( x \) values, and there will not be a point where one curve is above the other.

Given this information, the correct interpretation 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 only greater than the growth rate of g(x) = 1.3^x to the right of their right-most intersection point.**

However, since they are the same function, the statement technically holds no validity; instead, Austin would observe that \( f(x) \) and \( g(x) \) are equal for all \( x \). Therefore, a more accurate statement could be, "Austin should observe that both functions are identical and will not differ at any point."