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Quick Quick: Exponential function model needed!

Started by Grizwald Dec 21, 2004 at 4:58 PM 4 replies 550+ views

Original Post

Dec 21, 2004 at 4:58 PM

All i know is its an exponential function. I used to know it last year, and now i want to do it to make some image filters. Here is an ascii version of the shape.


             /---------------  y= 1
             * Vertical tangent line
y = 0 ______/

asymptotes are shown as y=blah. I cannot remember this for the life of me! EDIT: And no, I don't want a cube-root function... Those don't have the asymptotes

SiCrane

Dec 21, 2004 at 5:41 PM

Do you mean the sigmoid function ?

y = 1 / ( 1 + e ^-x )

kSquared

Dec 21, 2004 at 5:44 PM

Quote:
Original post by SiCrane
Do you mean the sigmoid function ?

y = 1 / ( 1 + e ^-x )

I thought of that too, but it doesn't have the vertical tangent he's looking for. Offhand, I can't think of that many exponential functions with vertical tangents, unless you're going to cheat with piecewise functions.

SiCrane

Dec 21, 2004 at 5:48 PM

Hmm. From his ascii art, I didn't think he wanted a perfectly verticle tangent line, there seems to be some slope at the point of tangent. Of course, using ascii art isn't exactly the best method to convey mathematical intent. :)

Grizwald

Dec 21, 2004 at 10:38 PM

OMG THANK YOU SO MUCH!
That was eating me away.

I was mistaken, there is no vertical tangent, but it will suit me even better without! Rating++ for you SiCrane!

nagromo

Dec 21, 2004 at 11:16 PM

I had just found one with a vertical tangent, too.

I like SiCrane's better, but here is something I found:

x=-(y-.5)^3/(y^2-y)

If you graph it it has the right shape, but neither my TI-89 or I can solve for y.

It seems more 'realistic' to use a sigmoid, though.

I'm still curious about how to solve that for y, but hey, I'm glad you found what you were looking for.

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