I have a table of values, how can I make an equation for them?

Question

These are the values:

0 | 1 | 2 | 3 | 4 | 5 | 6 |
4 | 6 | 7 | 7.5 | 7.75 | 7.875 | 7.9375 |

(Excuse my crappy table making skills!)

The top row is X and the bottom is Y, the pattern will continue. I think the equation will be an exponential one but I am unsure.

Thank you for your help.

Answer 1

y(0) = 4
y(1) = 4 + 2
y(2) = 4 + 2 + 1
y(3) = 4 + 2 + 1 + 1/2

This is a geometric series.
The term corresponding to x will be a(1 - r^n)/(1-r), where a=4, r=(1/2) and n=(x+1)
y = 4(1-(1/2)^(x+1))/(1-(1/2))
y = 8(1-(1/2)^(x+1)))

Answer 2

0 = 512
1 = 512 + 258
2 = 512 + 258 + 64
3 = 512 + 258 + 64 + 32
4 = 512 + 258 + 64 + 32 + 16
5 = 512 + 258 + 64 + 32 + 16 + 8
6 = 512 + 258 + 64 + 32 + 16 + 8 + 4
7 = 512 + 258 + 64 + 32 + 16 + 8 + 4 + 2
8 = 512 + 258 + 64 + 32 + 16 + 8 + 4 + 2 + 1

Answer 3

this is a geometric sequence with an equation of
Tn=6*1.5to the power of (n-1)