Your Practice Set – Applications and Interpretation for IBDP Mathematics
10
Paper 2 – Comparing Two Models
Example
The number of insects in two colonies , A and B , starts increasing at the same time .
The number of insects in colony A after t months is modeled by the function A( t) 240
0.3t
� e .
( a ) Find the initial number of insects in colony A .
( b ) Find the number of insects in colony A after seven months .
( c ) How long does it take for the number of insects in colony A to reach 800 ?
The number of insects in colony B after t months is modeled by the function B( t) � 360e kt .
[ 2 ]
[ 2 ]
[ 3 ]
( d ) After ten months , there are 1000 insects in colony B . Find the value of k . [ 3 ]
The number of insects in colony A first exceeds the number of insects in colony B after
n months , where n� .
( e ) Find the value of n . [ 4 ]
Solution
( a ) Initial number of insects 0.3 ( 0 )
� 240e ( A1 ) for substitution
� 240 A1
( b ) Number of insects in colony A after seven months
0.3 ( 7 )
� 240e
( A1 ) for substitution
� 1959.880779 � 1960
A1
[ 2 ]
[ 2 ]
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