Final answer:
Thomas Malthus posited a population crisis due to the arithmetic growth of the food supply and geometric expansion of the population, which could lead to Malthusian catastrophe when population surpasses food production, resulting in famines and wars. The correct answer is food supply increases arithmetically and the population expands geometrically.
Step-by-step explanation:
The Reverend Thomas Robert Malthus suggested that there would be a population crisis because the food supply increases arithmetically and the population expands geometrically. Malthus's theory proposed that while population could double each generation (2, 4, 8, 16, and so on), food production could only increase by the same amount over each time period (2, 4, 6, 8, etc.). He predicted that this disparity between the growth of population and food production would eventually lead to a situation where the population would surpass what the food supply could sustain, resulting in what is known as a Malthusian catastrophe, characterized by famine, disease, and war to reduce the population to sustainable levels.
In modern times, several factors such as technological advances in agriculture, the development of new medicines, and the use of contraception have alleviated some of these pressures, but concerns remain that the earth's resources will not be able to support an ever-growing human population indefinitely. Despite Malthus's grim predictions, human ingenuity has thus far expanded the food supply beyond the rates he anticipated.