Question

the values in the table represent an exponential function. what is the common ratio of the associated geometric sequence? x: 1, 2, 3, 4, 5 y: 22, 38, 54, 70.

Answer 1

Explanation:

I think it just a linear function and it's y=16x+6

Answer 2

`y = 16x+6` is the equation

common difference = 16

Explanation:

Given is a table which represent a function.

`x   1    2    3    4    5\\y   22 38  54  70   ...\\dx   1   1    1     1\\dy   16 16  16`

where dx represents change in x and dy represents change in y.

We see that
`(dy)/(dx) = 16 = constant`

Hence x and y have a linear relation with slope 16.

So equation would have the form

`y=16x+b`

Substitute x=1 and y =22, we get

`b=6\\y = 16x+6`