It is hoped that this paper will stimulate further analysis of various numerical information contained in Scripture to help clarify any seeming paradoxes centered around such numbers. The results of such analyses likely may well have sermon applications beyond the details of the specific passages in question.
I think this issue has serious ramifications for the exegesis of the numbers of the Exodus. Many if not most commentators simply assume exaggerated numbers. They have not crunched any numbers. My father shows that exaggeration is surely not necessary in order to understand the census numbers literally in the Exodus and Numbers account. What follows here is an abbreviated summary that my father wrote, and the article itself is available here (scroll to the attachment near the bottom).
The purpose of this paper was to demonstrate (with a mathematical model) how the population of the Israelites could have increased during their captivity in Egypt consistent with the specific census numbers noted in the book of Numbers. In particular, it was shown that a family size of 6-8 children throughout the time of captivity could easily account for the census numbers without resorting to metaphorical and/or hyperbolic interpretations of those numbers.
The mathematical model was characterized by the relaxing of any implicit extra Biblical requirement that the number of generations of all lines of all the patriarchs had to be limited to five during the entire time of captivity. The model was designed to include such parameters as the average number of children per family, the rate at which the first born and subsequent male children were killed by the Egyptians, the number of live births per family before and after the Egyptian edict, and a variable associated with multiple births, all of which resulted in a range of the total Israelite population being ~1.4 million to ~1.8 million, with the most likely number being around 1.5 million at the time of the Exodus from Egypt. In all cases, the census numbers in the book of Numbers were forced to be satisfied exactly by the calculational mechanism of the model.
Dr. J. C. Keister taught at Covenant College from 1970-1984 (teaching math, physics, logic, and judo). He got his Ph.D. in Physics from Georgetown University. He retired two years ago, and is currently living just south of Minneapolis.