Let me start of by saying I'm not sure if I'm going to be asking this question correctly. I want to find a way to make a formula that grows like a Cumulative distribution function like in this picture maybe about 1.
enter image description here Let me also reiterate that I remember very little about calculus.

So I want a formula that can get me something that looks like lambda = 1. I want the y axis to start at 0.5 and go all the way up to 3. I also want the x axis to start at 0 and go up to 2,500,000. If you have any idea how to make this possible I would love to know.

Before others asked if I have looked more into this I have. I've looked at some videos trying to get any explanation I could possibly use. I've looked at the formula on the Wikipedia page found here. I just don't know how to interrupt the formula.

  • $\begingroup$ Is there anyway to bump this? I might be asking this question wrong but I still want to know if I can get help here. $\endgroup$ – John Doe Dec 11 '17 at 0:12

The Wikipedia page you cite says the CDF is $1-e^{-\lambda x}$. $x$ is the lower axis. If you like $\lambda=1$ it is just $1-e^{-x}$

To have $y=0.5$ when $x=0$ you can add $0.5$ to the function. To increase the range to $2.5$ you can multiply by that, giving $$y=2.5(1-e^{-x})+0.5$$ $x$ can be as high as you want. $y$ will always be less than $3$, but gets close rather quickly.

  • $\begingroup$ But 24 and up will all be 1 and I don't want that. I want y to have a max of 3 and x to have a max of 2,500,000. And I want y to have a min of 0.5 and x to have a min of 0. So I want a formula where f(0) = 0.5 and then f(2,500,000) = 3. But I don't want it to be linear I want a curve similar to the image i have. I don't know how to use that formula to make one similar. $\endgroup$ – John Doe Dec 10 '17 at 1:42

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