Modelling Population Growth?
The population of a certain city is growing at a rate proportional to the current population. If the initial population is 1,00,000 and the growth rate is 5% per year, use the appropriate definite integral to find the population after 10 years.
1 Answer
📌 CONCEPT: The population growth can be modelled using the differential equation dP/dt = kP, where P is the population at time t and k is the growth rate per unit time.
📐 RULE / FORMULA: The solution to this differential equation is P(t) = P0 * e^(kt), where P0 is the initial population.
💡 WORKED EXAMPLE: Given P0 = 1,00,000 and k = 0.05, the population after 10 years is P(10) = 1,00,000 * e^(0.05*10) = 1,67,925.91.
⚠️ COMMON MISTAKE: Students often forget to use the correct growth rate and initial population values, or fail to evaluate the exponential function correctly.
09 Jun 26
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