I'd highly recommend Stark's book to anyone interested in topic. I've also read MacMullen's books on the subject, but Stark was
still a major eye opener!
As far as the numbers, it depends on what you are looking for. Obviously exact numbers in any year are only an estimate however they are derived, but the pattern of growth has to be roughly as depicted by that chart. Social phenomena grow by contact with outsiders and therefore exhibit exponential growth (i.e. growth isn't fixed in absolute terms but instead depends on the existing
membership size - it can be expressed as a percentage of the existing
membership).
The size of the
Christian population therefore naturally follows an exponential curve (notwithstanding any variation in the exact percentage growth in any given year or period), and the
average growth rate is very heavily bounded by the known facts. In 40AD we know that the number of Christians was very small, whether it was 100, 1000 or 10,000 - I'm sure nobody would claim it was 100,000 or larger. Similarly by 350AD we know that Christian's comprised a sizable percentage of the population; it's hard to imagine
Theodosius having been able to make Christianity the official state religion if Christians weren't of the order of 50% of the population (i.e. 30,000,000). You could argue the exact number, but again noone is going to suggest that the
Christian population in 350AD was less than say 25% or more than say 75%.
The formula for exponential growth is Nt = N0 x (1 + r) ^ t where N0 is the starting size (population), Nt is the population after t periods of growth, and r is the fractional growth rate
per period.
e.g. If we assume that in 40AD N0 = 1000 and r = 3.42% / yr (= 40% / decade), then the population in 350AD would be 1000 * 1.0342^310 = 33,682,581
You can also invert the formula to get the growth rate given the end points:
r = ((Nt / N0) ^ (1/t)) - 1 (as a fraction - multiply by 100 to get a percentage)
So for example:
with a starting population of 100 ending with 30,000,000 after 300 years growth, r = 4.29% / yr
with a starting population of 1000 ending with 30,000,000 after 300 years growth, r = 3.49% / yr
with a starting population of 10000 ending with 30,000,000 after 300 years growth, r = 2.70% / yr
So an annual growth rate of approx 3.5% (= 40%
per decade) has to be in the ballpark regardless of the exact starting numbers, and while the precise curve will vary, bottom line is that with an exponential growth rate in that ballbark the curve is always going to be roughly the same if it is the big picture you are looking for.
Interestingly as Stark notes, the 40% / decade (3.42% / yr) growth figure that seems to be in the ballpark for Christianity to have grown to 50% of the population by 350AD is also about the exact same
per decade figure that the Mormon religion has grown in the US over the last century (and no doubt that feels quite different whether one is in Utah or
New York, just as it would have done in
Antioch vs Trier).
Anyway, I highly recommend the book - it's much more than just statistics (the above examples are just my own, not from the book), and there is also much grounding as reality check for the numbers .
Ben