3 . Let x and y be the populations , in thousands , of leopard and crocodile in a habitat respectively . The changes in the populations can be modelled by the coupled differential �dx
�( 5 �8 yx )
� dt
equations �
.
�dy
�( 7x�3 ) y
�� dt
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The initial populations of leopard and crocodile are both 500 .
( a ) State , at the beginning , whether the population of crocodile is increasing or decreasing .
Euler ’ s method with a step length of 0.2 is used to approximate the populations of leopard and crocodile when t � 0.2 .
[ 1 ]
( b ) Find , when t � 0.2 , the approximate value of the population of
( i ) leopard ;
( ii ) crocodile . [ 4 ]
4 . Let x and y be the number of soldiers , in hundreds , from country X and country Y respectively . The changes in the number of soldiers in a battle between the two countries
can be modelled by the coupled differential equations
�dx
�( 12 �5 yx )
� dt
�
.
�dy
�( 3x�10 ) y
�� dt
( a ) When y � 0, state the range of values of x such that d y
0 dt � . [ 1 ]
The initial numbers of soldiers from the two countries are both 300 . Euler ’ s method with a step length of 0.1 is used to approximate the numbers of soldiers from the two countries
when t � 0.1.
( b ) Find , when t � 0.1, the approximate numbers of soldiers from
( i ) country X ;
( ii ) country Y . [ 4 ] www . seprodstore . com
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