World Population Growth

Population growth was one of the topics in the maths syllabus. The reason for this is that it relates the following branches of maths.

• binomial theorem

• Infinite series

• exponential function

• differential equations

However this produces an inconvenient truth for evolutionists when applied to world population.

This is an average growth rate of 0.7% per annum between the years 1830 to 1927 etc.

The Continuous % growth rate is calculated from the formula produced at the end of this page.

Example 1 Taking a growth rate of just 1% how long would it take to produce 6 billion people starting with just 2 people?

P=6x10⁹, P₀ =2, r=0.01
giving 6x10⁹=2.e^0.01t

make t the subject to give 0.01t = ln(3x10⁹)

giving t = 2182 years.

Of course we know that the population has been around for longer than that. This however shows how quickly the population can grow. Some Asian countries had a growth rate over 10% last century in spite of poor sanitation, poor sewerage disposal, disease epidemics and malaria etc

Example 2 Taking a very low growth rate of just 0.5% how long would it take to produce 6 billion people starting with just 2 people?

Similar calculations to the above produce a time of 4364 years ago which is about the flood of Noah. If the average growth rate was just 0.5% then the population growth rate must have been negative for very long periods of time as the growth rate has been over 1% when the population had grown very large.

Example 3 Taking a very low growth rate of just 0.5% and with just 2 people, what would the population size be after 10,000 years? (The time of the last supposed ice age?)

P₀ =2, t= 10,000, r=0.005 giving P=2.e^10000x0.005 , so P=2e⁵⁰ = 10²² an impossibly large number of people.

You can see why this produces an inconvenient truth for evolutionists.

The shortest way to produce the formula is using a differential equation.

Population growth dP/dt is proportional to the population size P. This is written as

dP/dt = rP where r is a constant

rearrange this to give

(1/P).dP = r . dt , integrate each side

∫(1/P).dP = ∫ r dt

to give

ln (P) = r.t + c , where c is the constant of integration

Make P the subject of this equation to give

P = e^rt+c ,

or P = e^rt.e^c

at t=0, P=P₀

giving P₀ = e⁰.e^c

or P₀ = e^c

Our population growth formula then becomes

Where P is the population size after t years starting with P₀ people growing at a continuous rate of r% per annum with r expressed as a decimal.