ESP168a.f10.lecture4.09.30.10

ESP168a.f10.lecture4.09.30.10 - ESP168a EnvironmentalPolicy...

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ESP 168a Environmental Policy  Analysis Lecture 4:  Difference Equations Joan Ogden September 30, 2010 jmogden@ucdavis.edu
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Difference Equations Use mathematical expressions to explore how things change over time
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Difference equations use discrete time intervals t=0 t=1 t=2 t=3 …………. . t=n
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Examples of difference equations Each year a fraction f of car owners buy a new car. Another fraction q scrap their cars. If we start in year 0 with C0 = 1000 cars, how many cars are in the fleet in year 1? C0=1000 C1=C0 x (1 +f –q) C2 = C1 x (1+f-q) = C0 x (1+f-q) 2
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Examples of difference equations If f=6% and q = 7% C0=1000 C1=C0 x (1 +f –q) = 1000 x (1+.06-.07)=990 C2 = C1 x (1+f-q) = C0 x (1+f-q) 2 = 980
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Examples of difference equations If the number of cars grows by 100 each year because people move to the city, how does the number change each year? C
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ESP168a.f10.lecture4.09.30.10 - ESP168a EnvironmentalPolicy...

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