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

It looks like there may be some confusion in the statements provided, especially with the representation of the functions \( h(x) \) and \( j(x) \). Both functions actually appear to be the same: \( h(x) = 1.2^x \) and \( j(x) = 1.2^x \).

If that is the case, here's how Liam should analyze the situation:

Liam should compare the rates of change of the terms in both sequences. Since the functions \( h(x) \) and \( j(x) \) represent the same exponential growth, they will grow at the same rate. Therefore, there isn't one that surpasses the other—they will always be equal.

To condense this into a response in line with the options provided, the following statement would best reflect the nature of the functions:

Liam should compare the rates of change of the terms in both sequences. The growth rate of \( j(x) = 1.2^x \) is equal to the growth rate of \( h(x) = 1.2^x \).

Unfortunately, that exact formulation is not present in your choices. None of the options correctly state that the growth rates of \( h(x) \) and \( j(x) \) are equal. So, if you had to choose based on your existing options, the one that emphasizes comparison of growth rates (even if it states that one surpasses the other) would be the best fit, but the confusion may lead to incorrect conclusions.

Thus, in summary, the attributes of both sequences are the same, and their growth rates will not surpass or differ from each other since they are identical functions.

Answer 2

I have to choose one out of the following answers given

Answer 3

Understood! Based on the provided options and given that both functions \( h(x) = 1.2^x \) and \( j(x) = 1.2^x \) are equivalent, here's a breakdown of your options:

1. 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.

2. Liam should compare the rates of change of the terms in both sequences. The growth rate of j times x is equal to 1.2 to the x th power will quickly surpass the growth rate of h of x is equal to 1.2 x.

3. Liam should look at where one sequence has terms greater than the terms in the other sequence. The growth rate of j(x)=1.2^x is only greater than the growth rate of h(x)=1.2^x when its terms are greater.

4. 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 1.2 to the x th power is only greater than the growth rate of h of x is equal to 1.2 x when its terms are greater.

5. Liam should look at where one sequence has terms greater than the terms in the other sequence. The growth rate of h(x)=1.2^x is only greater than the growth rate of j(x)=1.2^x when its terms are greater.

6. 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 1.2 x is only greater than the growth rate of j times x is equal to 1.2 to the x th power when its terms are greater.

7. 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)=1.2^x.

The best choice among these options 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)=1.2^x.

Although this statement is not correct (because \( j(x) \) and \( h(x) \) are identical), it at least includes the idea of comparing the growth rates, making it a marginally better choice compared to the other options which suggest that one sequence's terms exceed the other’s in growth rates.

If you’re required to choose one option, that would be it.