Forecasting decay rate - preventing negative values

Hi,

I am developing a series of forecasts for health care services using historical per capita rates as the source data.  In some areas, there has been a rapid decline in use.  When this is forecast using a standard linear regression model the values quickly become negative.  Given that these are unrealistic results (you can't have negative health care services), I have capped the values at zero.

In this instance, there will always be some usage.  What is a sensible way to determine a floor value that is greater than zero?

Here is a chart to illustrate.