The amount of "over-exposure" you will need for the backdrop depends upon the color of the backdrop material. If it is already some design of white backdrop item like flowers backdrop white background s-3049, you could get by by using enough extra light to have an over-exposure of approximately half an f-stop. Possibly even one full f-stop.
If the material you are beginning with is gray…that's OK too! Simply hit it with roughly 2 ½ stops (give or take) more brightness than you're using on the model.
Here's one that may blow several minds…what if your photography background fabric is really a pure black piece of material – or black paper?
This is a BUNCH of light and I wouldn't advocate starting with a black backdrop. When you start nearer to white in the beginning, it is a lot less difficult. Nevertheless, try it! It is a fun experiment and can educate you quite a bit on the subject of light!
By that I mean the further the light is from a subject matter, the less bright it appears.
Thus, meaning… if you have a certain quantity of light striking your subject matter, and you're using that SAME light to light your backdrop, your light is further away from your backdrop than from your model. Therefore, it is going to be a little dimmer when it gets to your background substance.
The main reason you're shooting that gray color is that there is more light striking your subject than is hitting the photography background.
To have your backdrop be a genuine, flawless white…simply hit it with MORE illumination than you are using for the model!