How to modify the function $y=a-be^{-cx}$ so that it will look wavy? [ other forms can be suggested ]
The function $y=a-(2+\sin x)be^{-cx}$ will work. The $2$ can be changed to any number $\ge1$ and the limiting value will still be an upper bound for the function; if it's changed to exactly $1$, the upper bound will be attained over and over again.