into World Population Growth Barring disasters (human-made or natural), the population \( P \) of humans grows at a rate proportional to its current size. According to the U.N. World Population studies, from 2005 to 2010 the population of the more developed regions of the world (Europe, North America, Australia, New Zealand, and Japan) grew at an annual rate of \( 0.409 \% \) per year. (a) Write a differential equation that models the growth rate of the population. (b) Find the general solution to the differential equation. (c) Find the particular solution to the differential equation if in \( 2010(t=0) \), the population of the more developed regions of the world was \( 1.2359 \times 10^{9} \). (d) If the rate of growth continues to follow this model, what is the projected population of the more developed regions in 2020 ? cn...n. IIN Wrld Ponulation Prospects, 2010 update.

The concept of population growth is rooted in Malthusian theory, conceived by Thomas Robert Malthus in the late 18th century. He proposed that populations grow exponentially while resources grow at an arithmetic rate, leading to inevitable conflicts between population and resources if unchecked. Modern interpretations take this idea further, applying mathematical models to various factors affecting growth rates, such as fertility, mortality, and migration, thereby providing a clearer picture of population dynamics over time. To really wrap your head around population growth, consider its real-world implications! Cities and countries face various challenges based on their population numbers: increased demand for housing, strain on healthcare systems, and pressure on education resources. For instance, places like Tokyo and New York constantly adapt to accommodate millions of residents. Population forecasts help governments plan infrastructure and social services wisely, ensuring that they can meet the growing needs of their populations—it's a delicate balancing act that influences everything from policy-making to urban planning!