Math In The Bible Session 1: Estimating Population Growth

Math In The Bible Session 1 Estimating Population Growth After Noah

In this assignment, we explore the application of the Fibonacci sequence to estimate the growth of animal populations following the biblical account of the flood in Genesis. We operate under the assumptions that each pair of animals reproduces once annually, with no death, starting with an initial number of pairs (A0). The purpose is to approximate population expansion over specific time frames, understanding the limitations and approximations inherent in such a model.

Questions and Answers

Question 1:

Given there are 7 animal pairs of each kind loaded onto Noah’s Ark (A0 = 7), how many animal pairs of each kind could we expect in year 20 and year 40?

The Fibonacci sequence models the population growth, beginning with A0 = 7. Using the sequence's properties, the number of pairs at year n is calculated by multiplying the Fibonacci number F(n) by 7. Based on the Fibonacci sequence, the Fibonacci numbers for year 20 and 40 are:

  • F(20) = 6765
  • F(40) = 102334155

Therefore, the population estimates are:

  • Year 20: 7 x 6765 = 47,355 animal pairs
  • Year 40: 7 x 102334155 = 716,339,085 animal pairs

This exponential growth demonstrates how quickly populations can expand when assuming uninterrupted reproduction and no mortality.

Question 2:

If Noah loaded 500 kinds of animals, totaling 3500 animal pairs (A0 = 3500), in what year does the model predict the total number of animal pairs reaches 10,000,000?

The initial total is A0 = 3500, and the growth follows the Fibonacci sequence. To find the year when total animal pairs reach or exceed 10 million, we find the Fibonacci number F(n) where:

3500 x F(n) ≥ 10,000,000

Rearranged, F(n) ≥ 10,000,000 / 3500 ≈ 2857.14

From Fibonacci number tables or calculations, F(17) = 1597, F(18) = 2584, and F(19) = 4181. Since F(18) = 2584, which is less than 2857.14, and F(19) = 4181, which exceeds 2857.14, the threshold is exceeded at year 19.

Thus, the total animal pairs would reach approximately:

  • Year 19: 3500 x 4181 ≈ 14,633,500 pairs

Therefore, the model predicts that the population surpasses 10 million animal pairs around the 19th year after the flood.

Summary and Observations

This exercise illustrates the explosive nature of exponential population growth modeled through Fibonacci numbers, emphasizing how small initial populations can, under idealized conditions, grow to enormous sizes within relatively short periods. The model's assumptions—constant reproduction rate, no mortality, and unlimited resources—are highly optimistic and do not reflect real ecological constraints. Nonetheless, this mathematical approach offers insight into the potential scale of animal populations after Noah's Ark, as well as underscores the importance of demographic factors in population dynamics.

Such models, while simplified, can be useful pedagogical tools for understanding exponential growth and its implications in biological contexts, including conservation biology and epidemiology. The biblical narrative provides a foundation for engaging with mathematical concepts through historical and religious texts, enriching both fields of study.

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