Chapter3a - CIVL1005 - Environmental Engineering...

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1 CIVL1005 - Environmental Engineering Mathematics of Growth Mathematics of Growth Office: Rm. 6-30, Haking Wong Building Phone: 2859-1973 E-mail: kshih@hku.hk Dr. Kaimin Shih DEPARTMENT OF CIVIL ENGINEERING THE UNIVERSITY OF HONG KONG • Exponential Growth • Resource Consumption • Human Population Growth - OUTLINES -
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2 What do they have in common? What do they have in common? A sense of the future is essential in influencing many decisions we make today… 德国汤若望( Johann Adam Schall von Bell )顺治皇帝钦天监 A wastewater treatment plant : Predict the growth rate of bacteria in a pollutants digester tank “ We cannot expect to make accurate predictions of the future. ” A local power generation facility : Predict the local population growth rate over next decays Scientist and policy maker : Estimate deforestation & reforestation rates due to global warming But, we can use simple mathematic models to develop very useful “what if“ scenarios.
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3 Exponential Growth N 0 = Initial amount N t = amount after t years R = growth rate (fraction per year) N t+1 = N t + R N t = N t (1+R) N t+1 = N 0 (1+ R ); N 2 = N 1 (1+ R ) = N 0 (1+ R ) 2 N t = N 0 (1+ R ) t or, N t = N 0 e rt ( by letting e r = 1 + R ) Exponential growth - simple, common & important Increase in some quantity is proportional to the amount currently present (a particular case of a first order rate process).
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4 Continuous Compounding When to use exponential growth? Doubling Time
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Chapter3a - CIVL1005 - Environmental Engineering...

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