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

Answer:

Option  D

Step-by-step explanation:

Let an exponential function

$f(x)=ab^x$

Where a=Constant$\neq 0$

$b\neq 0$

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)

$2=b^1$

$\implies b^2=4\neq 5$

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.