Math Equation question

I was wondering about something today and my calculus teacher didn’t help much so I decided that this was the best place to ask. What would the equation be for a function that would go through the points: [1,1], [2,.5], [3,.25], [4,.125], and so on so that for every increase of one in the x direction the y value halves itself from the previous time. I figured that it would have to be a logarithm graph or a hyperbola but I could figure out the equation. Any help?

Sorry, that was supposed to read “I could not figure out the equation or graph”.

y = 5[sup](x - 1)[/sup] ?

well…i figure it’s the same as :

x + a = y * (1/2)^a

if thats any help. I’m not in a good thinking mood tonightmand the only was i can think of is with a third variable. Hmm… youk now that there is a vertical asymtote(sp) at 0. I know a vertical asymtote means the function is undefined at x= 0… which means there an x in the denominator of something. I guess some math wizard will figure it out for you.

You know, I would almost have sounded half-intelligent if i had taken the time to proof-read my post before I sent it in.

I think you mean y = 2[sup](x - 1)[/sup]

I believe y = 2[sup]-(x-1)[/sup] fits those data points.

x=1; y = 2[sup]0[/sup] = 1

x=2; y = 2[sup]-1[/sup] = 1/2 = 0.5

x=3; y = [sup]-2[/sup] = 1/4 = 0.25

x=4; y = [sup]-3[/sup] = 1/8 = 0.125


y = 2sup[/sup] would fit your data set.

I honestly didn’t see the decimal points in the range. (Now it’s my eyesight, what will fail next?! :()

And I honestly can’t believe that I made a sign error in my attempted correction of you.