Answer:
[tex]y = 2(4)^{x}[/tex]
Step-by-step explanation:
The relation is not linear as the change in the value of y with the unit change of x is not uniform.
So, the relationship is exponential.
Let us assume that the relationship is [tex]y = a\times b^{x}[/tex] ........ (1) where we have to find a and b from the given values in the table.
For, x = 0, y = 2
Therefore, from equation (1) we get
a = 2.
Now, for x = 1, y = 8 and for x = 2, y = 32.
Therefore, [tex]8 = a \times b^{1} = ab[/tex] .......... (2) and
[tex]32 = a \times b^{2} = ab^{2}[/tex] ........... (3)
Now, dividing equation (3) with equation (2) we get,
[tex]\frac{ab^{2} }{ab} = \frac{32}{8}[/tex]
⇒ b = 4
Therefore, the final equation is [tex]y = 2(4)^{x}[/tex] (Answer)
