Apps. and Interpretation for IBDP Maths Ebook 1 | Page 48

Your Practice Set – Applications and Interpretation for IBDP Mathematics
12
Paper 1 – Exponential Models
Example
The number of elephants P in a small jungle is modelled by
t is the number of years after 2015.
1
t
35
e �
P( t) �170 � 90 , where
(a) Write down the number of elephants in 2015.
[1]
(b) Find the number of elephants in 2019, giving the answer correct to the nearest
integer.
[2]
(c) Find the number of years needed after 2015 when the number of elephants first
exceeds 140.
[2]
(d) Write down the minimum value of the upper bound of the number of elephants.
[1]
Solution
(a) 80 A1 N1
(b)
(c)
The number of elephants
1 (4)
170 90e � 35
� � (M1) for substitution
� 89.71972447
� 90
A1 N2
1
t
35
e �
170 �90 � 140
(M1) for valid approach
1
t
35
e �
30 �90 � 0
By considering the graph of
1
t
35
e �
y�30 � 90 ,
t � 38.45143 .
Thus, the number of years needed is 38.5 years. A1 N2
(d) 170 A1 N1
[1]
[2]
[2]
[1]
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