Question

Kareem wants to write an equation for the data in the table below.

Answer 1

the answer is:

y = ab^x


the proper answer is:
( y = 2^x)

Answer 2

We are given with the table of x and y values

We use the given y values to find the required equation

When the first difference between the y values are same then it is linear.

When the common ratio between y values are same then it is exponential.

When the second difference of y values are same then it is quadratic.

Lets find the difference between y values

`(1)/(4) - (1)/(8) = (1)/(8)`

`(1)/(2) - (1)/(4) = (1)/(4)`

`1 - (1)/(2) = (1)/(2)`

The difference is not same . so we cannot choose y= mx+b

Now we find the common difference between y values

`((1)/(4))/((1)/(8)) = 2`

`((1)/(2))/((1)/(4)) = 2`

`(1)/((1)/(2)) = 2`

The common ratio is 2. So its exponential.

The required equation
`y=ab^x`