please help me with this :(

Question

Explain how you know the data in the table below does not represent an exponential function.

x	0	1	2	3
y	2	6	24	120

 

Answer 1

From above table (x,y) points are (0,2) , (1,6) , (2,24) , (3,120).

Let general exponential function is y = ab^x

y = ab^x passes through (0,2)     ⇒  2 = ab⁰   ⇒ a = 2

y = ab^x passes through (1,6)     ⇒  6 = ab¹   ⇒ b = 6/a  ⇒ b = 6/2 ⇒ b =3.

y = ab^x passes through (2,24)   ⇒  24 = ab²  ⇒ b² = 24/a ⇒ b² = 24/2 ⇒ b =2√3.

y = ab^x passes through (3,120) ⇒  120 = ab³ ⇒ b³ = 120/a ⇒ b³ = 120/2 ⇒ b = 2√15.

For any exponential function a , b values are constant.

But here b value is a variable (not a constant).

So data in the table does not representing an exponential function.