Question

What is the equation?

Answer 1

Answer:

$y = 2(4)^{x}$

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 $y = a\times b^{x}$ ........ (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, $8 = a \times b^{1} = ab$ .......... (2) and  

$32 = a \times b^{2} = ab^{2}$ ........... (3)

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

$\frac{ab^{2} }{ab} = \frac{32}{8}$

⇒ b = 4  

Therefore, the final equation is $y = 2(4)^{x}$ (Answer)