Question

Which set of ordered pairs could be generated by an exponential function?A.(0,0),(1,1),(2,8),(3,27)B.(0,1),(1,2),(2,5),(3,10)C.(0,0),(1,3),(2,6),(3,9)D.(0,1),(1,3),(2,9),(3,27)

Answer 1

Option D

Explanation:

Let an exponential function

`f(x)=ab^x`

Where a=Constant
`\\eq 0`

`b\\eq 0`

We know that

`b^0=1`

Therefore,

Point (0,0) can not be obtained by exponential function.

Hence,option A and C are incorrect.

Substitute (0,1)

`1=a`

`f(x)=b^x`

Substitute (1,2)

`2=b^1`

`\implies b^2=4\\eq 5`

Hence, option B is incorrect.

D.(0,1),(1,3),(2,9),(3,27)

`f(1)=b=3`

`b^2=(3)^2=9`

`b^3=3^3=27`

Hence, option D is correct.