Your Practice Set – Applications and Interpretation for IBDP Mathematics
8
Paper 1 – Logistic Functions
Example
The population Pt () of a town t years after 1st January , 2017 can be modelled by 200
Pt () � 1 4 , t � 0 . � t
e �
( a ) Find the population at the beginning of
( i ) 2017 ;
( ii ) 2021 .
( b ) Write down the range of Pt ().
[ 4 ]
[ 2 ]
Solution
( a ) |
( i ) |
The population at the beginning of 2017 |
|
|
�
P ( 0 )
|
|
200
�
0 1 �
4e �
|
( M1 ) for substitution |
|
�
40
|
A1 |
( ii ) The population at the beginning of 2021 � P ( 4 )
200
� ( M1 ) for substitution
4
1 � 4e � � 186.3476919 � 186
A1
( b ) { P: 40 �P� 200 }
A2
[ 4 ]
[ 2 ]
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