Question

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)
Responses

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

Answer 1

To correctly compare the growth rates of the functions \( h(x) = 1.2x \) (which represents linear growth) and \( j(x) = 1.2^x \) (which represents exponential growth), Liam should focus on their respective growth behaviors.

The correct statement is:

**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 exponential functions grow faster than linear functions as \( x \) increases. Therefore, as \( x \) becomes larger, the terms in the sequence defined by \( j(x) \) will quickly outpace those of the sequence defined by \( h(x) \).