Using exponential function concepts, it is found that f(x) increases faster than g(x) on the interval of 0 < x < 1.
An exponential function is modeled by:
[tex]y = ab^x[/tex]
In which:
In the interval of 0 < x < 1, a lower value of b leads to a greater change, while for x > 1, a higher value of b leads to greater change.
In this problem, the functions are:
[tex]f(x) = 2^x[/tex]
[tex]g(x) = \left(\frac{8}{3}\right)^x[/tex]
Hence:
[tex]b_f = 2[tex]
[tex]b_g = \frac{8}{3}[/tex]
Since [tex]b_g > b_f[/tex], f(x) increases faster than g(x) on the interval of 0 < x < 1.
More can be learned about exponential function concepts at https://brainly.com/question/25537936
