Download Population Growth Model: Exponential Growth and Recursive Equations and more Study Guides, Projects, Research Introduction to Business Management in PDF only on Docsity! Project Grant Team John S. Pazdar Patricia L. Hirschy Project Director Principal Investigator Capital Community College Asnuntuck Community College Hartford, Connecticut Enfield, Connecticut This project was supported, in part, by the Peter A. Wursthorn National Science Foundation Principal Investigator Opinions expressed are those of the authors Capital Community College and not necessarily those of the Foundation Hartford, Connecticut SPINOFFS Spinoffs are relatively short learning modules inspired by the LTAs. They can be easily implemented to support student learning in courses ranging from prealgebra through calculus. The Spinoffs typically give students an opportunity to use mathematics in a real world context. LTA - SPINOFF 15A The Capture-Recapture Method LTA - SPINOFF 15B Florida Scrub-Jay Populations and Habitat LTA - SPINOFF 15C Population Models with Recursive Equations Brian Smith - AMATYC Writing Team Member McGill University, Montreal, Quebec, Canada Mario Triola - AMATYC Writing Team Member Dutchess Community College, Poughkeepsie, New York Janet Rebmann - NASA Scientist/Engineer Kennedy Space Center, Florida NASA - AMATYC - NSF 15 . 27 SPINOFF 15C Population Models with Recursive Equations Mathematical models are important tools for monitoring and forecasting future population sizes. Four key factors affecting population size are: • Birth rate • Death rate • Immigration rate • Emigration rate These components are affected by habitat conditions such as human activity, fire, predators, drought, vegetation, etc. In the NASA Kennedy Space Center surroundings, long-term effects include the environmental impact of “multiple launches and continuing land use changes.” (http://atlas.ksc.nasa.gov/program.html). Mathematical models incorporating all relevant components are extremely complex, but useful models may be constructed by including the four key factors listed above. Because births and immigration increase the population size, and deaths and emigration decrease it, a simple model can be described as follows: New Population Size = (Previous Population Size) + (Births) − (Deaths) + (Immigration) − (Emigration). Each term in this equation is based on a given time interval (a day, a year, etc.). We can represent the above terms with the following mathematical symbols: N t+1 = New population size (population size at time t + 1) N t = Previous population size (population size at time t) B = Number of births in one time unit D = Number of deaths in one time unit I = Number of new immigrants entering the population in one time unit E = Number of emigrants leaving the population in one time unit Using these symbols, we can rewrite the equation as follows: t+1 tN = N + B D + I E− − In a closed system we assume that there is no migration into or out of the system so that the equation becomes: t+1 tN = N + B D − In this model we may define the rate of growth as 0r = (B D)/N− , where N 0 is the population at time t = 0. As a result, we assume a constant rate of growth during the time interval. If the number of births
