Maybe fitting a, b, c  to formula:

f(t) = { 1-exp [ -(a+bt )] } exp (-ct ), with positive a, and non-negative b and c

will do the job?  Found in: Seung Won Hyun, Min Yang, Nancy Flournoy,

A procedure for finding an improved upper bound on the number of optimal design points,

Computational Statistics & Data Analysis 58 (2013) 276,

http://dx.doi.org/10.1016/j.csda.2012.08.012