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 \( h(x) \).
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