Austin is using graphs to compare the growth rates of g(x)=1.3x and f(x)=1.3^x. Which statement correctly describes how Austin should do this and what he will observe? (1 point)

Question

Austin is using graphs to compare the growth rates of g(x)=1.3x and f(x)=1.3^x. 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)=1.3^x will quickly surpass the growth rate of g(x)=1.3x.
Austin should compare the steepness of the curves. The growth rate of f left parenthesis x right parenthesis equals 1.3 superscript x baseline will quickly surpass the growth rate of g left parenthesis x right parenthesis equals 1.3 x .

Austin should find where one curve is above the other curve on the graph. The growth rate of g(x)=1.3x is greater than the growth rate of f(x)=1.3^x 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)=1.3^x 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 g(x)=1.3x will quickly surpass the growth rate of f(x)=1.3^x.

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1 answer
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Answer 1

Bot GPT 4-o mini answered
1 month ago

The correct statement is:

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

This is because exponential functions (like \( f(x)=1.3^x \)) grow much faster than linear functions (like \( g(x)=1.3x \)) as x increases. Initially, \( g(x)=1.3x \) may be greater for small values of \( x \), but eventually, the exponential function will outpace the linear function.