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Message: <blockquote data-quote="Hankook" data-source="post: 30015083" data-attributes="member: 580311">If we assume zero mortality rates, no migration, and only fertility rates influence population growth, we can estimate when Sri Lankan Moors might surpass the Sinhalese in population percentage.Here’s a simplified approach to the calculation:Initial Populations and Fertility Rates:Sinhalese: 75%Moors: 9%Sinhalese fertility rate: 2.3Moor fertility rate: 3.3Population Growth Model:The population of a group grows according to the formula P(t) = P_0 \times (1 + r)^tP(t)=P 0 ×(1+r) t , where P(t)P(t) is the population at time tt, P_0P 0  is the initial population, and rr is the growth rate (which in this simplified model is \text{fertility rate} - 1fertility rate−1).Growth Rates:Sinhalese growth rate: 2.3 - 1 = 1.32.3−1=1.3Moors growth rate: 3.3 - 1 = 2.33.3−1=2.3Projection:Let P_{\text{Sinhalese}}(t)P Sinhalese (t) and P_{\text{Moors}}(t)P Moors (t) represent the population proportions of Sinhalese and Moors at time tt, respectively. We have:P_{\text{Sinhalese}}(t) = 0.75 \times (1 + 1.3)^tP Sinhalese (t)=0.75×(1+1.3) t P_{\text{Moors}}(t) = 0.09 \times (1 + 2.3)^tP Moors (t)=0.09×(1+2.3) t We want to find tt when P_{\text{Moors}}(t)P Moors (t) exceeds P_{\text{Sinhalese}}(t)P Sinhalese (t).Solving:Set up the inequality:0.09 \times (1 + 2.3)^t > 0.75 \times (1 + 1.3)^t0.09×(1+2.3) t >0.75×(1+1.3) t 0.09 \times 3.3^t > 0.75 \times 2.3^t0.09×3.3 t >0.75×2.3 t \frac{0.09}{0.75} > \left(\frac{2.3}{3.3}\right)^t0.750.09 >( 3.32.3 ) t 0.12 > \left(\frac{2.3}{3.3}\right)^t0.12>( 3.32.3 ) t \left(\frac{2.3}{3.3}\right)^t < 0.12( 3.32.3 ) t <0.12Taking natural logs on both sides to solve for tt:\log\left(\left(\frac{2.3}{3.3}\right)^t\right) < \log(0.12)log(( 3.32.3 ) t )<log(0.12)t \cdot \log\left(\frac{2.3}{3.3}\right) < \log(0.12)t⋅log( 3.32.3 )<log(0.12)t > \frac{\log(0.12)}{\log\left(\frac{2.3}{3.3}\right)}t> log( 3.32.3 )log(0.12) Plugging in the values:\log(0.12) \approx -0.921log(0.12)≈−0.921\log\left(\frac{2.3}{3.3}\right) \approx -0.274log( 3.32.3 )≈−0.274t > \frac{-0.921}{-0.274} \approx 3.36t> −0.274−0.921 ≈3.36So, in this simplified model, the Moors would surpass the Sinhalese in about 3 to 4 periods of growth, or roughly 3 to 4 cycles of population doubling.Assuming a 10-year cycle for simplicity, it would take approximately 30 to 40 years for the Moors to surpass the Sinhalese in population percentagewise.</blockquote>

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