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

$\frac{1}{4} - \frac{1}{8} = \frac{1}{8}$

$\frac{1}{2} - \frac{1}{4} = \frac{1}{4}$

$1 - \frac{1}{2} = \frac{1}{2}$

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

Now we find the common difference between y values

$\frac{\frac{1}{4}}{\frac{1}{8}} = 2$

$\frac{\frac{1}{2}}{\frac{1}{4}} = 2$

$\frac{1}{\frac{1}{2}} = 2$

The common ratio is 2. So its exponential.

The required equation $y=ab^x$