Ben Shaver

2022-01-06

Which set of ordered pairs could be generated by an exponential function?
A. (1, 1) (2, 1/2) (3, 1/3) (4, 1/4)
B. (1, 1) (2, 1/4) (3, 1/9) (4 1/16)
C. (1, 1/2) (2, 1/4) (3, 1/8) (4, 1/16)
D. (1, 1/2) (2, 1/4) (3, 1/6) (4, 1/8)

Kirsten Davis

Determine the ration of each pair of consecutive y-values for each option
Option A
$\frac{\frac{1}{2}}{1}=\frac{1}{2}=0.5$
$\frac{\frac{1}{3}}{\frac{1}{2}}=\frac{2}{3}\approx 0.66$
$\frac{\frac{1}{4}}{\frac{1}{3}}=\frac{3}{4}=0.75$
Option B
$\frac{\frac{1}{4}}{1}=\frac{1}{4}=0.25$
$\frac{\frac{1}{9}}{\frac{1}{4}}=\frac{4}{9}\approx 0.44$
$\frac{\frac{1}{16}}{\frac{1}{9}}=\frac{9}{16}=0.5625$
Option C
$\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{2}{4}=\frac{1}{2}=0.5$
$\frac{\frac{1}{8}}{\frac{1}{4}}=\frac{4}{8}=\frac{1}{2}=0.5$
$\frac{\frac{1}{16}}{\frac{1}{8}}=\frac{8}{16}=\frac{1}{2}=0.5$
Option D
$\frac{\frac{1}{4}}{\frac{1}{2}}=\frac{2}{4}=\frac{1}{2}=0.5$
$\frac{\frac{1}{6}}{\frac{1}{4}}=\frac{4}{6}=\frac{2}{3}\approx 0.6667$
$\frac{\frac{1}{8}}{\frac{1}{6}}=\frac{6}{8}=\frac{3}{4}=0.75$
Thus, we can see, that we have a constant answer for the option C, and it can be generated by an exponential function.

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