# Which set of ordered pairs could be generated by an

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)

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