Use the table to answer the question.

Question

Term Number 1 2 3 4 5 6
Sequence for
g(x)=20x
20 40 60 80 100 120
Sequence for
f(x)=2x
2 4 8 16 32 64
Zoya is comparing the growth rates of g(x)=20x
and f(x)=2x
using their sequences as shown in the table. They notice that the terms of f(x)=2x
are always less than the terms of g(x)=20x
and so conclude that f(x)=2x
grows slower than g(x)=20x
. Where is their mistake in comparing the growth rates?

(1 point)
Responses

Zoya must have calculated the growth rates incorrectly. Both functions are growing at the same rate.
Zoya must have calculated the growth rates incorrectly. Both functions are growing at the same rate.

Zoya has it backward. The growth rate of f(x)=2x
is always greater than the growth rate of g(x)=20x
.
Zoya has it backward. The growth rate of f left parenthesis x right parenthesis equals 2 superscript x baseline is always greater than the growth rate of g left parenthesis x right parenthesis equals 20 x .

Zoya should be comparing the differences between the values of the terms in each sequence as opposed to just comparing the values of each sequence.
Zoya should be comparing the differences between the values of the terms in each sequence as opposed to just comparing the values of each sequence.

Zoya should have made a bigger table. If they did, they would have seen that the terms of f(x)=2x
are eventually greater than the terms of g(x)=20x
.

Answer 1

Zoya's mistake in comparing the growth rates of g(x)=20x and f(x)=2x is that they are comparing the values of each sequence instead of comparing the differences between the values of the terms in each sequence. In this case, the growth rates of the two functions are the same because they both increase linearly with the input x. The mistake could have been avoided if Zoya compared the differences between the terms rather than the actual values of each sequence.