Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 10
1 . The number of leopards and tigers in a forest start increasing at the same time .
The number of leopards in the forest after t years is modeled by the function A( t) 2500e
0.075t
� .
( a ) Find the initial number of leopards .
( b ) Find the number of leopards after ten years .
( c ) How long does it take for the number of leopards to reach 8000 ?
The number of tigers in the forest after t years is modeled by the function where k � 2000 .
180 t k
B() t � ke ,
[ 2 ]
[ 2 ]
[ 3 ]
( d ) After ten years , there are 5000 tigers . Find the value of k . [ 3 ]
( e ) The number of tigers first exceeds the number of leopards after n years , where
n� . Find the value of n . [ 4 ]
2 . The number of trams and the number of people using trams in a city is studied .
The number of trams in the city after t years is modeled by the function At ( ) �420� 1.15 t .
( a ) Find the initial number of trams .
( b ) Find the number of trams after six years .
( c ) How long does it take for the number of trams to reach 750 ?
The number of people using trams in the city after t years is modeled by the function 4680000
Bt () � . kt 70e � �130
[ 2 ]
[ 2 ]
[ 3 ]
( d ) After five years , there are 27500 people using trams . Find the value of k .
( e ) The number of trams first exceeds five times the number of people using trams after n years , where n� . Find the value of n .
[ 4 ]
[ 4 ]
32
SE Production Limited