Liam is using sequences to compare the growth rates of h(x)=1.2x and j(x)=1.2x . Which statement correctly describes how Liam should do this and what he will observe?(1 point)

Question

Responses

Liam should look at where one sequence has terms greater than the terms in the other sequence. The growth rate of j(x)=1.2x is only greater than the growth rate of h(x)=1.2x when its terms are greater.
Liam should look at where one sequence has terms greater than the terms in the other sequence. The growth rate of j left parenthesis x right parenthesis equals 1.2 superscript x baseline is only greater than the growth rate of h left parenthesis x right parenthesis equals 1.2 x when its terms are greater.

Liam should compare the rates of change of the terms in both sequences. The growth rate of h(x)=1.2x will quickly surpass the growth rate of j(x)=1.2x.
Liam should compare the rates of change of the terms in both sequences. The growth rate of h left parenthesis x right parenthesis equals 1.2 x will quickly surpass the growth rate of j left parenthesis x right parenthesis equals 1.2 superscript x baseline .

Liam should compare the rates of change of the terms in both sequences. The growth rate of j(x)=1.2x will quickly surpass the growth rate of h(x)=1.2x.
Liam should compare the rates of change of the terms in both sequences. The growth rate of j left parenthesis x right parenthesis equals 1.2 superscript x baseline will quickly surpass the growth rate of h left parenthesis x right parenthesis equals 1.2 x .

Liam should look at where one sequence has terms greater than the terms in the other sequence. The growth rate of h(x)=1.2x is greater than the growth rate of j(x)=1.2x when its terms are greater.

Answer 1

To correctly compare the growth rates of the functions \( h(x) = 1.2x \) (a linear function) and \( j(x) = 1.2^x \) (an exponential function), Liam should:

Liam should compare the rates of change of the terms in both sequences. The growth rate of j(x)=1.2^x will quickly surpass the growth rate of h(x)=1.2x.

This is because the exponential function \( j(x) = 1.2^x \) grows faster than the linear function \( h(x) = 1.2x \) as \( x \) increases. Initially, for small values of \( x \), \( h(x) \) may be larger, but eventually \( j(x) \) will surpass it and continue to grow at a much faster rate.