Question

What is the equation?

Answer 1

`y = 2(4)^(x)`

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
`y = a* b^(x)` ........ (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,
`8 = a * b^(1) = ab` .......... (2) and

`32 = a * b^(2) = ab^(2)` ........... (3)

Now, dividing equation (3) with equation (2) we get,

`(ab^(2) )/(ab) = (32)/(8)`

⇒ b = 4

Therefore, the final equation is
`y = 2(4)^(x)` (Answer)