SEM`L 6). . ``DO`\LE $ 5. 6 . 1 ( C) How long will it take until the population is one- half its 1 . Assume a discrete - time population whose size
Calculus help with questions: 2, 4, 8, 10, 14, 16, 20, 24.
SEM`L 6). . ``DO`\LE$ 5. 6 . 1( C) How long will it take until the population is one- half its1 . Assume a discrete - time population whose size at generationoriginal size ?I + 1 is related to the size of the population at generation + by5 . Assume the discrete - time population modelNit1 = ( 1. 03 ) N . . {1 = 0 . 1 . 2 , . .NITI = ON1. 1 = 0 . 1 , 2 ,( a) If No = 10 , how large will the population be at generationAssume that the population increases by * % each generation .1 = 5 ?`( a ) Determine b .( b ) How many generations will it take for the population size to( 10) After how many generations will the population size havereach double the size at generation O ?*doubled ? Compute the doubling time for* * = 0.1 , 0. 5 , 1 , 2 , 5 ,2 . Suppose a discrete - time population evolves according toand 10 .*6 . ( a ) Find all equilibria ofNit1 = ( 0.9 ) No. 1 = 0 . 1 . 2 . . ..NITI = 1.3 N . .`* = 0 . 1 , 2 . ..( a ) If No = 50 , how large will the population be at generation1 = 6 ?( 1 ) Use cobwebbing to determine the stability of the equilibria( b ) After how many generations will the size of the populationyou found in ( a ) .be one- quarter of its original size ?7 . ( a ) Find all equilibria of( C ) What will happen to the population in the long run - that is ,Nit1 = O. ON . .`1 = 0 . 1 , 2 . .`as 1 - 00 ?3 . Assume the discrete - time population model( 6 ) Use cobwebbing to determine the stability of the equilibriayou found in ( a ) .\NITI = ON1, 1 = 0 . 1 . 2 . ..8 . ( a ) Find all equilibria ofAssume also that the population increases by 2% each generation .NITI = N1, 1 = 0 . 1 , 2 . . .`( a ) Determine b .( b ) Find the size of the population at generation 10 when No =\( b ) How will the population size N , change over time , starting at20 .time O with No ?!( C ) After how many generations will the population size have$ 5 . 6. 2doubled ?`9 . Use the stability criterion to characterize the stability of the4 . Assume the discrete - time population modelequilibria ofNITI = ON . . 1 = 0 . 1 , 2 . ....Xit! = -* = 0 , 1 , 2 , . .Assume also that the population decreases by 3% eachgeneration .10 . Use the stability criterion to characterize the stability of the( a ) Determine b .equilibria ofE( 10 ) Find the size of the population at generation 10 when No =50 .X/ +1 =\1 = 0 . 1 , 2 ,
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