Which set of ordered pairs could be generated by an exponential function?

(1, 1), (2, one-half), (3, one-third), (4, one-fourth)

(1, 1), (2, one-fourth), (3, one-ninth), (4, one-sixteenth)

(1, one-half), (2, one-fourth), (3, one-eighth), (4, one-sixteenth)

(1, one-half), (2, one-fourth), (3, one-sixth), (4, one-eighth)

C.(1,one-half),(2,one-fourth),(3,one-eight),(4,one-sixteenth)

Step-by-step explanation:

We have to find the set of ordered pair which could be generated by an exponential function.

We know that the range of exponential function is in geometric progression.

When the sequence is geometric then the ratio of consecutive two term is constant.

In first option

Let

It is not in G.P.

Hence, it is not the set of ordered pairs which could be generated by an exponential function.

In second function

It is not in G.P

Hence, it is not the set of ordered pairs which could be generated by an exponential function.

In III option

It is in G.P

Hence, it is the set of ordered pairs which could be generated by an exponential function.

In IV option

It is not in G.P

Hence, it is not the set of ordered pairs which could be generated by an exponential function.

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