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

Question

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 h(x)=1.2x will quickly surpass the growth rate of j(x)=1.2x

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 h(x)=1.2x is greater than the growth rate of j(x)=1.2x when its terms are greater.

Answer 1

To 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 note that exponential functions typically grow faster than linear functions as \( x \) increases.

Among the provided statements, the following is the correct one:

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 statement accurately describes that the exponential growth of \( j(x) \) will eventually exceed the linear growth of \( h(x) \) as \( x \) becomes larger.