Sometimes an Atheist will argue that there could not have been enough people to build the Tower of Babel or to have been slaves in Egypt under Pharoah. Here is an example of how this can be answered.

You bring up three historical events and something that you see as a problem regarding population growth. I would like to allow you to discover something about arbitrary assumptions.

We know the following by revelation: There were somewhere over 100 years between the beginning of the flood and the Tower of Babel, but God has not told us exactly. There were somewhere over 1,000 years between the beginning of the flood and the time of Moses. Life was greatly extended (400-600 years) for a while after the flood. They were commanded to multiply. There were 4 couples on the Ark.

The math is rather simple, but you would have to make some arbitrary assumptions about what would be possible if you were going to say that something is impossible. Whenever you are trying to prove something to be impossible, you must make assumptions that are most in favor of the thing being possible and then show that, even given those assumptions, the thing is impossible. It is very common for zealous people to take the opposite route--to make assumptions that are designed to constrain whatever is being shown to be impossible and then to make believe that the thing has been shown to be impossible. Such a tactic is irrational, however.

What would you assume to be a generation, the age at which people started having children? 14? 18? 22? What is the shortest possible? 12? 14? They didn't have to go to school or prepare to become lawyers. Let’s assume 16.

What would you assume to be the average family size? 7? 10? 20? What is the largest possible with the extended lifespans and pure gene pool. 20? 30? Let’s assume 10 per couple or 5 per person.

What would you assume to be the length of time between the flood and the Tower. 106? 120? Let’s assume 106, so 106/16=a little over 6 generations.

On the Ark = 8 people = 4 couples

1^st generation = 40

2^nd generation =  200

3^rd generation = 1,000

4^th generation = 5,000

5^th generation = 15,000

6^th generation = 125,000

All of that is immaterial, because of the following most important point:

What would you assume was the number of people working on the Tower of Babel? 10? 50? 100? 1,000?

There is no problem. It is a manufactured dilemma based on assumptions.

There is particularly no problem of "not enough people to be slaves of Pharaoh" about 900 years later, even with decreasing lifespans and more disease, wars, etc. as people turned away from God. All of the false dilemma is caused by irrational thinking and believing arbitrary assumptions.