Liam is using sequences to compare the growth rates of h(x)=1.2x

Question

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 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 of x is equal to 1 point 2 x will quickly surpass the growth rate of j times x is equal to 1 point 2 to the x th power

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 times x is equal to 1 point 2 to the x th power is only greater than the growth rate of h of x is equal to 1 point 2 x when its terms are greater.

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 times x is equal to 1 point 2 to the x th power will quickly surpass the growth rate of h of x is equal to 1 point 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 only 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 of x is equal to 1 point 2 x is only greater than the growth rate of j times x is equal to 1 point 2 to the x th power when its terms are greater.
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Answer 1

To clarify, it seems there is a small confusion in the expressions for the functions. Based on the choices provided, the functions being compared appear to be:

• \( h(x) = 1.2^x \) (an exponential function)
• \( j(x) = 1.2x \) (a linear function)

Given this understanding, the correct statement would involve exploring the growth rates of these two types of functions.

The exponential function \( h(x) = 1.2^x \) will ultimately outpace the linear function \( j(x) = 1.2x \) as \( x \) increases because exponential growth eventually surpasses linear growth.

Therefore, the correct response would be:

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 response aptly captures the nature of the functions and their growth rates.