A value that increases in a curvy way?

Hi guys, I have this game where the speed of a ball depends on the level. Now I want to increase the speed of the ball each level but not in a direct way. I want to do it in a curvy way. What kind of algorithm can I use for such thing? Sorry If my words don't make sense to you, Here's a couple of graphs :

What I can already do :


What I want to do :


Thanks in advance fellas

 

You can solve this problem in many different ways.
First is to write a function that contains mathematical function of a curve you desire. By the look at your figure it is logarithmical function.
it would go something like this:

private float someConstant = 3.0f;
private float logarithmicBase = 2.0f;
private float getCurrentSpeed(float level) {
return (someConstant * Mathf.Log(level, logarithmicBase));
}

You should figure values for someConstat na logarithmicBase in a way that suits your needs.

The other option is to Use AnimationCurve - http://docs.unity3d.com/ScriptReference/AnimationCurve.html
There you can draw your curve and call current value in script.

 

AnimationCurve is probably your best option as tweaking it, as well as visualizing the curve, is very straight forward and easy.

 

Thanks for the great answers, you have no idea how much these helped me