Up to a point your channel should snowball, so you should gradually see an increase in daily subscribers. There are so many variables though, nothing is guaranteed. You may just hit on a video that goes viral and be catapulted to thousands of subs in a matter of days or you may continue to grow at the same rate for years. There is no magic number that you can say "after 500 subs I started to grow more quickly" or "once I published my 50th video my channel exploded".
Since you have little to no control over many of the factors that will influence the growth of your channel it is best to focus on the things that you DO have control over; consistent, high quality content that engages your viewers.