Question

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 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 left parenthesis x right parenthesis equals 1.3 x will quickly surpass the growth rate of f left parenthesis x right parenthesis equals 1.3 superscript x baseline .

Austin should find where one curve is above the other curve on the graph. The growth rate of g(x)=1.3x
is greater than the growth rate of f(x)=1.3x
between the intersection points of the curve.
Austin should find where one curve is above the other curve on the graph. The growth rate of g left parenthesis x right parenthesis equals 1.3 x is greater than the growth rate of f left parenthesis x right parenthesis equals 1.3 superscript x baseline between the intersection points of the curve.

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 left parenthesis x right parenthesis equals 1.3 superscript x baseline is only greater than the growth rate of g left parenthesis x right parenthesis equals 1.3 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
.

Answer 1

It appears there is a typographical error in your functions. It looks like you are trying to compare \(g(x) = 1.3^x\) and \(f(x) = 1.3^x\) (where both functions seem to be the same). However, if you meant to compare an exponential function with a linear function, you might have intended \(g(x) = 1.3^x\) (which grows exponentially) and \(f(x) = 1.3x\) (which grows linearly).

Assuming that is the case, the correct statement should be:

"Austin should compare the steepness of the curves. The growth rate of \(g(x) = 1.3^x\) will quickly surpass the growth rate of \(f(x) = 1.3x\)."

If both functions are indeed the same, then growth rates are identical, and no comparison is necessary. Please clarify the functions to provide the most accurate answer.