@Stephen: @Random832 is correct, both "exponential" and "geometric" growth refer to having a constant ratio between successive/equidistant terms (which means the rate of growth is proportional to the current value - in calculus this is stated by saying an exponential function has f'(x) = c*f(x)).
In that case your minutes-per-level function would be polynomial (time = Level ^ c) or even exponential (time = c ^ Level). Taking the level-number as-is in an exponential formula is usually much too extreme, however.
And therefore the function is y=(x/2.390)^2. Notice that the same value can be used for the Green curve, and therefore that function would be -((x-200)/2.390)^2+7000. For the Red curve (exponential) you know that z^MAXIMUM LEVEL=MAXIMUM VALUE. Therefore you only need to calculate z as the MAXIMUM LEVEL'th root of MAXIMUM VALUE.
I stumbled upon this function that lerp towards a moving target with exponential correction which works really well. The original author mentioned integrating the target position. Can anyone explai...
Use a polynomial or exponential function. Do you want the value to grow fast at first, and slow down later? Use an nth-root or logarithmic function. Do you want the value to grow slowly at the start/end but fast in the middle? Or do you want it to grow quickly but still have an upper-bound? Use a sigmoid curve, such as atan or the logistic ...
You would use an exponential function for the acceleration to double the speed every second. I'm not sure if OP actually wants that. It will get out of hand quickly.
š Learn how to graph exponential functions involving horizontal shift. An exponential function is a function that increases rapidly as the value of x increases. To graph an exponential function, it ...