23. (a)Note that the given years correspond to x50,x520,x550,x570, andx580.y5}111.01785.7e020.0422x}[0, 100] by [0, 20](b)Carrying capacity 5limx→‘y518.70, representing 18.7 million people.(c)Using NDER twice and solving graphically, we findthat y050 when x < 1.7, corresponding to the year1912. The population at this time was about y(1.7) <9.35 million.24. (a)y5}117.12945.7e620.0513x}[0, 50] by [0, 15](b)Carrying capacity 5limx→‘y524.76, representing 24.76 million people.(c)Using NDER twice and solving graphically, we findthat y0 when x <38.44, corresponding to the year1988. The population at this time was about y(38.44) <12.38 million.25.}ddPt} 5 }Mk}P(M2P)}P(MMd2PP)} 5k dt}(MP(2MP2)1P)P}dP5k dt1}P1}1 }M21P}2dP5k dtln )P)2ln )M2P)5kt1Cln )}MP2P})5kt1Cln )}M2PP})52kt2C}M2PP}56e2Ce2kt}M2PP} 5Ae2ktM2P5APe2ktM5P(11Ae2kt)P5}11MAe2kt}26. (a)y5}115.11362.9e020.0666x}(b)Carrying capacity 5limx→‘y516.90 representing 16.9 million people.27.}ddyx} 5(cos x)esin xEdy5E(cos x)esin
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