Math Problem Statement
Assume the carrying capacity of the Earth is 18
billion. Use the 1960 annual growth rate of 2.1 % and population of 3
billion to predict the base growth rate and current growth rate with a logistic model. Assume a current world population of 7.8
billion. How does the predicted growth rate compare to the actual growth rate of about 1.1 % per year?
Solution
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Math Problem Analysis
Mathematical Concepts
Logistic Growth Model
Population Dynamics
Formulas
Logistic Growth Equation: dP/dt = rP(1 - P/K)
Base Growth Rate: r₀ = r(1 - P₀/K)
Current Growth Rate: r_current = r(1 - P/K)
Theorems
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Suitable Grade Level
Grades 11-12 (Advanced High School) or Undergraduate Level
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