Use the table to answer the 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
.