Please help! need to create formula 1element =5 dbi every time the element doubles you +3 dbi

Question

Example

So

1. 1 Element =( 5) dbi
2. 2 Element = 5+3. (8) dbi
3. 4 Element = 5+3+3 (11) dbi
4. 8 Element = 5+3+3+3 (14) dbi
5. 16 Element = 5+3+3+3+3 (17) dbi

Other example

2² Element = 5+3+3. (11) dbi

4² Element = 5+3+3+3+3 (17) dbi

Answer 1

I won't pretend this is the true answer, but I'll give you this for thought...

If "n" is the index column from 1 thru 5, the number of elements is 2^(n-1)

2^(1-1) = 1

2^(5-1) = 16

One the "dbi" side of the equations, the number of dbi is 5 + 3 * (n - 1)

5+3*(1-1) = 5

5+3*(5-1) = 17

Let's combine this two into a formula:

dbi/element = 2^(n-1) / (5+3*(n-1))

where n=1 you get 1/5

where n=5 you get 16/17

If that's not the right answer, does it at least lead you to a better one?