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

Question

ℎ
(
𝑥
)
=
1.2
𝑥
and j(x)=1.2x
𝑗
(
𝑥
)
=
1.2
𝑥
. 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
𝑗
(
𝑥
)
=
1.2
𝑥
will quickly surpass the growth rate of h(x)=1.2x
ℎ
(
𝑥
)
=
1.2
𝑥
.
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
𝑗
(
𝑥
)
=
1.2
𝑥
is only greater than the growth rate of h(x)=1.2x
ℎ
(
𝑥
)
=
1.2
𝑥
when its terms are greater.
Liam should look at where

Answer 1

The statements in your question seem to be regarding exponential expressions in terms of growth rates. However, it looks like you have a mistake in your definitions, as both \( h(x) \) and \( j(x) \) appear to be the same function, \( 1.2^x \).

Assuming you meant two different functions, perhaps comparing \( h(x) = 1.2^x \) (which is an exponential function) and \( j(x) = 2^x \) (another exponential function), here’s how Liam would compare their growth rates:

Correct Approach and Observation: Liam should compare the growth rates of \( h(x) \) and \( j(x) \) by examining the behavior of these functions as \( x \) increases. Specifically, he will observe that the growth rate of \( j(x) = 2^x \) will eventually surpass the growth rate of \( h(x) = 1.2^x \) because exponential functions with larger bases grow faster than those with smaller bases as \( x \) increases.

If both functions were indeed meant to be \( h(x) = 1.2^x \) and \( j(x) = 1.2^x \), then both sequences have the same growth rate and will always match each other at all values of \( x \).

If you would like a more detailed explanation or if there are any clarifications, please let me know!

Answer 2

answer

Answer 3

Based on the context provided, the correct statement that describes how Liam should compare the growth rates of the sequences and what he will observe 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 \( h(x) = 1.2^x \).

If both functions are indeed supposed to be the same (i.e., \( h(x) = j(x) = 1.2^x \)), then they would have the same growth rate, and Liam would observe that their terms are equal for all values of \( x \).

If instead, the functions are different exponential functions (e.g., \( h(x) = 1.2^x \) and \( j(x) = 2^x \)), he should observe that the growth rate of \( j(x) \) surpasses that of \( h(x) \) as \( x \) increases because \( 2^x \) grows faster than \( 1.2^x \).

Please pick the first statement if the functions are the same, or clarify if there's a mix-up in the function definitions.