# Exponential approaches

Rough tool to map equations of the form value_{n} = value_{n-1} + (target - value_{n-1}) * *expFactor*

which depend on the number of iterations, to ones that
consume time deltas and behave a bit better with varying framerates value_{n} = target - (value_{n-1} - target) / e^{dt / timeHorizon}

[if a supporting blogpost were to exist, a link to it would be here]

Given *expFactor* and a framerate, you can adjust *timeHorizon* to make the functions match (for example, *timeHorizon* =
0.1485 matches *expFactor* = 0.2 with 30 fps). Support for different implementations of e^{x} is provided, though in practice a 3rd order Taylor series works well enough.

zoom

*expFactor*

*timeHorizon*

framerate

exponential function