When starting a custom game, under the Advanced tab you will find 4 options:

• Level Gain Curve
  
• Level Health Curve
  
• Research Gain Curve
  
• Research Cost Curve

These items have the values of 1.4, 1.4, 1.3, and 2.0 respectively. These numbers are the exponential increase rate. It means that at any given level you are 'Value' greater than the previous level. As an example lets look at the 'Level Health Curve' stat. This determines how many hitpoints a subsystem has for a given scale. Let us assume you have a blueprint designed where a subsystem you added gives you 10,000 hp exactly at its current scale and tech level. If you improved the related tech level exactly one higher that subsystem would now have 14,000hp at the exact same scale. ie: 1.4 times more. And if you gained one more tech level it would now have 19,600hp. Notice it did not just gain 4000 more hp. That would be a 'linear' increase. Since SR uses exponential growth gaining one more tech level makes the 14000 value get multiplied by 1.4. So each level is always worth more than the previous.

What does this mean for the Research Cost Curve? It means that every level will always cost exactly twice the total research points that the previous level cost. So level 2 is twice as expensive as level 1. level 3 is twice as expensive as level 2 (or 4x as expensive as level 1). Level 4 is double lvl 3 (which is 8x lvl 1). So if level 1 cost you 1000 research points, to get to level 4 would require 8000 + 4000 + 2000 == 14,000 additional experience points to achieve.

You'll notice that with a multiplier of 1.4 any given value ALMOST doubles every 2 levels. What if you want to tweak those values but you dont understand exponential growth very well yet? There is a simple formula (for you to put into a calculator) to determine the growth rate. Type this into your calculator:

X ^ ( 1 / Y )

For 'X' type how large of a growth you want, and for 'Y' type how many levels you want it to take to get that growth. So if you want a growth rate so that it takes 5 tech levels to double in value you would type the following in your calc:

2 ^ ( 1 / 5 )

You will get an answer of ~1.1487. If you wanted to find the value where tech WOULD exactly double ever 2 levels (instead of almost) you would enter:

2 ^ ( 1/2 )

And get ~1.4142. BTW for those curious this ratio that the game uses makes it so that at level 10 things you produce are 32 times better and at level 20 things you produce are 1024 times better than what you made with zero tech. If you plugged in 20 and 1024 into the formula I gave above it would list the same growth rate (1.4142) as the answer.

Hope that formula helps you understand exponential growth (and how to configure your game exactly how you want) better.