To compare the growth rates of the functions \( f(x) = 1.3^x \) and \( g(x) = 1.3x \), Austin should be aware that:
- \( f(x) = 1.3^x \) is an exponential function, which grows faster than any linear function as \( x \) increases.
- \( g(x) = 1.3x \) is a linear function.
Thus, 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 choice accurately describes the behavior of the functions as \( x \) increases, confirming that while \( g(x) \) may be larger for small values of \( x \), \( f(x) \) will eventually outpace \( g(x) \) as \( x \) becomes larger.