S2.6+-+Mathematics+of+Growth.pptx

S2.6+-+Mathematics+of+Growth.pptx - CEE 265 Sustainable...

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Brian R. Ellis Assistant Professor, Civil and Environmental Engineering S2.6 Mathematics of Growth CEE 265: Sustainable Engineering Principles
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Mathematics of Growth Compound Growth at Discrete Intervals at rate “r” per interval “Exponential” Growth at continuous intervals at rate “r” proportional to current population Doubling Time Disaggregated Growth Logistic Growth where exponential growth at first slowing to carrying capacity
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Growth and Sustainability First we’ll consider cases where the increase in some quantity is proportional to the amount currently present. Examples: Interest (interest applied at discrete intervals) Costs (higher education, debt, health care) Populations (populations at early stages continuously grow at a rate proportional to populations) Consumption (unenlightened consumption, particularly in rich countries, grows in proportion to the population) 3
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Compound Growth: Discrete Increments In-Class Problem (ICP) 2.6.1
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