noob question find formula for table of values

[jlmango]

x	g(x)
0.5	-1
1	0
2	1
4	2
8	3

I am trying to find a formula to describe this table. I used slope formula delta Y over delta X to determine if the rate of change was linear. It is not. I do not believe it is exponential since g(x) has the value of zero and exponential equations approach 0 but never cross. I entered the data into my calculator and performed quadratic regression and the formula turned out funky so I crossed out that possibility as well. I am in calc I and we are doing a bunch of review problems. Can you help me? I am stuck!

 

[jlmango]

is there a general formula or method I can use to find this other than realizing that the values are of base 2 exponents?

thanks a million for you reply!!!!

 

[galactus]

The closest regression this corresponds to is a log regression.

\(\displaystyle y=1.442695 \ln(x)\)

i.e. \(\displaystyle 1.442695 \ln(1/2)=-.999999971658\)

\(\displaystyle 1.442695 \ln(1)=0\)

.
.
.
\(\displaystyle 1.442695 \ln(8)=2.99999991497\)

This is pretty darn accurate. I doubt if we get any better than this.

Check them with your calculator.