Slow decreasing function that exhibits asymptotic behaviour I am currently doing some work on modelling the effects of treated nets usage on mosquito populations. Nets do not retain their maximum efficacy forever. They lose their chemical efficacy after about three years and all that is left is the physical protection offered by the net which I estimate to be $20\%$ of the original efficacy.
I am trying to model this behaviour. I need a continuous function over the interval $[0,1095]$ which decreases slowly  from 1 when $x=0$ and asymptotically approaches $0.2$ when $x \to 1095 $.
I tried an ellipse of the form $y=\sqrt{1-\dfrac{x^2}{(1095)^2}}$, but I realized the function is equal to zero when $x=1095$, which is not what I want.
Any help will be appreciated.

How about something like
$$
y=1-0.8\,\frac{e^{ax}-1}{e^{1095a}-1}?
$$
The sign of $a$ determines concavity or convexity; $a=-0.005$ gives a nice graph.
