What mathematical model can be used to predict the optimal location for a new capital city based on factors such as population distribution, geographical features, and economic activity?

What mathematical model can be used to analyze the exponential growth in the global consumption of coffee over the past century, and how has this growth affected coffee production and pricing in major coffee-producing countries?

Logistic growth model: C = C0 * (1 + r)^t / (1 + C0 * r * (e^(rt) - 1)), where C is consumption, C0 is initial consumption, r is growth rate, t is time, e is Euler's number

Mongolia is the most sparsely populated country — 2 people per square kilometer

Mongolia has a population density of approximately 2 people per square kilometer

The capital of Kazakhstan is Astana — renamed from Nur-Sultan back to Astana in 2022

Astana (renamed Nur-Sultan) is Kazakhstan's capital

What is the mathematical model behind the SIR (Susceptible, Infected, Recovered) epidemiological framework used to predict the spread of infectious diseases?

dS/dt = -βSI, dI/dt = βSI - γI, dR/dt = γI

The capital of Turkey is Ankara, not Istanbul — moved by Atatürk in 1923

Capital of Turkey: Ankara, established by Atatürk in 1923

The capital of Hungary is Budapest — originally two cities, Buda and Pest, merged in 1873

Budapest, formed from Buda and Pest in 1873, is Hungary's capital