Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 44
1 . The number of insects , n , after t months is given by
0.28t n � . 300e
( a ) Find the value of n when t � 0.
( b ) ( i ) Find d n dt .
[ 2 ]
( ii ) Hence , write down the rate at which n is increasing when t � 6.
[ 3 ] ( c ) After k months , the rate of increase in n is greater than 1000 insects per month .
Find the least value of k , where k � . [ 3 ]
2 . The volume of an object ,
3
V cm , t seconds after the start of an experiment is given by
V
2
� 100 � t , for 0 t 10 � � .
( a ) Find the value of V when t � 8 .
( b ) ( i ) Find d V dt .
[ 2 ]
( ii ) Hence , write down the rate at which V is decreasing when t � 6.
[ 3 ]
( c ) Within k seconds after the start of the experiment , the rate of decrease in V is smaller than
3 1
0.9 cm s � . Find the greatest value of k , where k � .
3 . The population of sheep in a farm , p , t months after 1 January 2019 is given by p� 250sin ( 2t� 3.9 ) � 750 .
( a ) Find the number of sheep in the farm on 1 June 2019 . [ 3 ]
( b ) Find d p dt . [ 2 ]
[ 3 ]
After n days , where n� time .
, the rate of increase in p is equal to 0 per month for the first
( c ) Find the value of n .
[ 3 ]
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