Liam is using sequences to compare the growth rates of h(x)=1.2xh(x)=1.2x and j(x)=1.2xj(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)=1.2xh(x)=1.2x will quickly surpass the growth rate of j(x)=1.2xj(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 compare the rates of change of the terms in both sequences. The growth rate of j(x)=1.2xj(x)=1.2x will quickly surpass the growth rate of h(x)=1.2xh(x)=1.2xLiam 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)=1.2xh(x)=1.2x is only greater than the growth rate of j(x)=1.2xj(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. Liam should look at where one sequence has terms greater than the terms in the other sequence. The growth rate of j(x)=1.2xj(x)=1.2x is only greater than the growth rate of h(x)=1.2xh(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.

Answer 1

To compare the growth rates of the functions \( h(x) = 1.2^x \) and \( j(x) = 1.2x \), Liam should analyze how the two sequences behave as \( x \) increases.

The correct approach is to observe the nature of the functions:

• \( h(x) = 1.2^x \) represents exponential growth, which accelerates as \( x \) becomes larger.
• \( j(x) = 1.2x \) is a linear function, which grows at a constant rate.

As \( x \) increases, the exponential function \( h(x) \) will grow significantly faster than the linear function \( j(x) \). Therefore, the statement that best describes Liam's comparison would be:

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

This captures the essence of the comparison, emphasizing that \( h(x) \) grows faster than \( j(x) \) as \( x \) increases.