Question

Liam is using sequences to compare the growth rates of h(x)=1.2x and j(x)=1.2x . Which statement correctly describes how Liam should do this and what he will observe?(1 point) 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 left parenthesis x right parenthesis equals 1.2 x will quickly surpass the growth rate of j left parenthesis x right parenthesis equals 1.2 superscript x baseline . 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 .

Answer 1

It looks like there is a misunderstanding in the notation and growth rates between the two functions. The growth rates of $h(x)=1.2x$ and $j(x)={1.2}^x$ are being compared.

In this case, the correct statement 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 is because $j(x)={1.2}^x$ is an exponential function, while $h(x)=1.2x$ is a linear function. Exponential functions grow much faster than linear functions as $x$ increases. Therefore, Liam will observe that as $x$ becomes large, the value of $j(x)$ will far exceed that of $h(x)$.