Analysis and Approaches for IBDP Maths Ebook 2 | Page 45

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Paper 2 Section A – Real Life Problems
Example
The total profit $y of selling plastic boxes can be modelled by the equation
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y � ax �bx � c , where x is the number of plastic boxes ordered from a factory, and a ,
b and c are real numbers. The total profits of selling 100 plastic boxes, 200 plastic boxes
and 400 plastic boxes are $122, $424 and $1628 respectively.
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(a) Write down three equations in a , b and c .
(b) Hence, find the values of a , b and c .
[3]
[2]
Solution
(a) 10000a �100b � c � 122
A1
40000a � 200b � c � 424
A1
160000 a � 400b �c
� 1628
A1
(b) a � 0.01, b � 0.02 and c � 20
For any one correct answer
A1
For all correct answers
A1
[3]
[2]
Exercise 12
1. The height h metres of a parachute t seconds after released from a helicopter can be
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modelled by h � at �bt � c , and a , b and c are real numbers. The heights of a
parachute at different times are shown in the following table:
t (s) 1 3 6
h (m) 998 982 928
(a) Write down three equations in a , b and c .
(b) Hence, find the values of a , b and c .
[3]
[2]
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