Assignment 1.docx
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1、t+h t ( ( r= CHENG Fangyuan ITSC ID:fcheng Student ID:20369816 Assignment 1 1. Since Y =Y er*h , so r=ln( + )/h (1) instantaneous rate: 1.000172% r=ln 2011 1981 )/30 =ln( 7.0716 5.2385 )/30 =0.01000172 (2) discrete rate: 1.005190% according to the discrete model, R=exp(r)-1 r= ln 2011 1981 )/30 =ln(
2、 7.0716 5.2385 )/30 =0.01000172 R=e0.01000172-1 =0.01005190 (3) central rate: 0.9927349% + - h*(+) 2 7.0716-5.2385 = 30*(7.0716+5.2385)/2 =0.009927349 These three rates are not much different. Y =Y e ( t+h T ( ( Doubling time r*h t+h T , so h=ln( + )/r 2 h= =69.3 0.01000172 The doubling time implied
3、 by the 1981 2011 growth rate is 70 years. Times that HKs population reaches a size of 10 million h=ln( + )/r =ln( 10 7.0716 )/ 0.01000172 =34.64 In 2046 HKs population will reach 10 million. Growth rate to reach 10million r=ln + )/h =ln( 2030 2011 )/19 10 = ln( )/19 7.0716 =0.018236754 1.82% is hig
4、h enough for HK population to grown to 10million by 2030. 2. According to the instantaneous growth rate model Y =Y er*h , the population growth rate r= ln + )/h, the population doubling time h= ln + 2 )/r= r 662 1950-1960: r= ln( 2 )/10=0.018171750, h= = 2 =38.14 552 r 0.018171750 830 1960-1970: r=
5、ln( )/10=0.022616014, h= 2 =30.6485 662 0.022616014 987 1970-1980: r= ln( )/10=0.017324434, h= 2 =48.39 830 0.017324434 1143 1980-1990: r= ln( )/10=0.014674162, h= 2 =47.24 987 0.014674162 1250 1990-2000: r= ln( )/10=0.008948717, h= 2 =77.46 1143 0.008948717 Decades Growth Rate(%) Doubling Time(year
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