By Mike Mesterton-Gibbons

ISBN-10: 0470171073

ISBN-13: 9780470171073

**Read or Download A Concrete Approach to Mathematical Modelling (Wiley-Interscience Paperback Series) PDF**

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Let us make the bold assumption that capital lasts forever. 9): Rate of Change of _ Capital Capital Stock ~~ Inflow Capital Outflow 0. 6 Economi c Growt h 19 Her e is a furthe r relation, a differentia l one. But by also introducin g an extr a function, namely, / ( i ) , we have moved no nearer t o closing our model! W e must therefore devise a new relation withou t introducin g new func› tions. A new relation requires a fresh assumption. Perhaps the simplest we can make is that the economy retains a constant proportion , σ, of output for it s capital stock.

46), because it says just as much with far less risk that it might actually be wrong. 46) suffices as a model. 10) is false! What can we do about mis? Notice from Fig. 6 that the short-term dynamics appears cyclic. 46). We might regard the short-term model as imbedded in the long-term one. 47) xn+l = B(yitb)), where y denotes pollution within a time unit and appropriate functions A, B, and g are to be defined. 47) is independent of n. 8 Salmo n Dynamic s 23 then t - t = 1 - f, - c . 47). Just suppose, for example, that our mischievous polluter achieves his goal by doubling the pollutio n level one tenth of a tim e unit after every reading, lettin g it decay at the natural rat e and then halving it again one tenth of a tim e unit before the next reading.

Dynamica l System * DIx -I 0 I I I I I I I I I 50 I I • 1 100 • 150 ' ' I I -’ ’ hv 200 Fig. S. population (horizontal axis) plotted against specific growth rate (verti › cal axis) for years 1800-1960. The unit of tim e is a decade; the unit of population, a million . 4. Notice that they are correct t o at least one significant figure unti l 1950. I n fact, the percentage error , that is, i. 5% throughout thi s entir e period, except for the year 1860, when the error i s a littl e over 5%. 4). 60) by about 20%.

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