[R] Nonlinear regression help

[Taylor Hermes]

I seek help with nonlinear regression for my data.  I've run intro
trouble fitting a model to my data as follows:

rate_parameter stable_population
75 1996.1277
100 1623.2979
125 1362.3475
150 1164.6738
175 1014.8227
200  892.0851
225  794.1844
250  710.1489
275  639.6738
300  578.0496
325  525.4965
350  479.4752
375  440.3050
400  402.4397

The "rate_parameter" here will be my independent variable which
affects the "stable_population" quantity in an agent-based simulation.

I can see that the plot of this data seems to fit an exponential
decay.  I would greatly appreciate if someone could help me out with
this task.  I've found the following info on this page helpful:
https://stat.ethz.ch/pipermail/r-help/2001-December/017330.html
yet, still unable to grasp what I need to do.

Thanks!