Analysis and Approaches for IBDP Maths Ebook 1 | Page 54

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(d) B(10) � 1000
(M1) for substitution
10k
360e � 1000
10k
360e �1000 � 0
10k
By considering the graph of y�360e
� 1000 (M1) for correct working
k � 0.1021651
�k
� 0.102
A1 N3
[3]
(e) A( t) � B( t)
(M1) for setting inequality
A( t) �B( t) � 0
0.3t
0.1021651 t
240e
�360e
� 0
By considering the graph of
0.3 0.1021651
240 t
y � e � 360e
(M1) for correct working
t � 2.0495125
(A1) for correct working
�n
� 3
A1 N3
[4]
Exercise 16
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
0.075t
A( t) � 2500e
.
(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]
[3]
[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]
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