Ok, so here’s a numerical example that shows that you cannot extrapolate population growth from birth rate without knowing the parents’ age. I will use an extreme example because my rebbe in numbers taught me to use extreme examples to pressure test calculations.
Constants: Birth rate per couple is 4 (so per person is 2). In other words, on average each person has 2 children between when they are born and when they die. We start in year 1 with 1 couple and calculate to year 100. Population growth will be calculated as the increase in percentage per year. Everyone lives until the year 100 and then all die. The first couple is Generation A, and so on.
Scenario 1: Generation A gives birth to quadruplets in year 1. Generation B each give birth to quadruplets in year 2. Generation C each gives birth to quadruplets in year 3. And so on for each of the 100 years.
Result 1:
Year 0: 2 people.
Year 1: 4 births.
Year 2: 8 births.
Year 3: 16 births.
Year 4: 32 births
5: 64
6: 128
7: 256
8: 512
9: 1024
10: 2048 Births
Year 100: Many many many
Population growth rate: Ask Charlie.
Scenario 2: Generation A gives birth to quadruplets in year 50. Generation B each give birth to quadruplets in year 100. And so on for each of the 100 years.
Year 0: 2 people
Year 1: 2 people
Year 2: 2 people
…
Year 50: 4 births
Year 51: 0 births
Year 52: 0 births
Year 100: 16 births!
Total people in year 100: 22
Population growth (22-2)/100