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

Question

. 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 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 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 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.

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

The correct statement regarding Liam's comparison of the growth rates of the functions \( h(x) = 1.2^x \) and \( j(x) = 1.2^x \) is the following:

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) = 1.2^x.

This statement accurately reflects that both functions represent the same exponential growth. However, since \( h(x) \) and \( j(x) \) are identical (both being \( 1.2^x \)), it indicates that their growth rates are equal rather than one surpassing the other. Therefore, Liam will observe that the growth rates of both functions are equivalent at all points.