I Don't know how to google what I want: An equation of smaller increments?

Question

Appologies, I'm no mathematician, so I don't even know what words to google to find equations. This is likely simple math.

I need to create a formula in a program that for an input of 1 I can get a result, As an example 50, but for 2 I get a result approx 75, and 3 might be 95, etc, and I can structure it so the last result of 500 might result in 500. I'm sure this is simple, yet I don't know what its called to even google it.

Thanks in advance, I only need the name so I can google it, but will happily discuss further if interested.

Answer 1

If I understand your question correctly, you want a continuous function that "increases with smaller increments" for greater inputs?

A simple exponential function might fit your application:

The curve above is an arbitrarily picked exponential function that roughly matches the model you described:

$$y=-e^{\left(\frac{500-x}{80}\right)}+500$$

Since you said wanted a name that you can google, consider following up on the keywords

• Exponential Growth
• Exponential Decay
• Logistic Growth
• Polynomial Growth

Exponential models are trivial to incorporate into programs (the application you mentioned in your question). Most modern languages include built-in or library support for exponentiation. For instance, in Python you have the exponential operator ** and the function math.exp. Java includes java.lang.Math.{exp,pow}, etc.