Analysis and Approaches for IBDP Maths Ebook 1 | Page 309

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(c)
The insurance cost
8
� 8352 �(1 � 3%)
(M1)(A1) for valid approach
8
� � (A1) for simplification
8352 0.97
� 6545.824538
� $6550
A1 N2
t
(d) 8352 �(1 �3%) � 5000
(M1) for setting equation
t
8352 �0.97 �5000 � 0
(A1) for simplification
t � 16.84427
(A1) for correct value
Thus, the year is 2036. A1 N2
[4]
[4]
Exercise 100
1. Yuto is a beekeeper who collected data about monthly honey production in his bee hives.
The data for five of his hives on 1 January 2018 is shown in the following table.
Number of bees ( x ) 490 620 750 815 830
Monthly honey production
( y kg)
1.3 1.5 1.7 2.2 2.8
The relationship between the variables is modelled by the regression line with equation
y �ax � b .
(a) (i) Find the correlation coefficient.
(ii) Write down the value of a and of b .
[4]
(b) Use the regression line to estimate the monthly honey production from a hive that
has 700 bees, giving your answer to the nearest 0.1 kg.
[3]
Starting from 1 January 2018, the monthly honey production from the hive in (b)
increased by 2% each month.
22
(c) Calculate the monthly honey production from the hive after 1 year.
[4]
Yuto will sell the hive to another farm when its monthly honey production reaches 3 kg.
(d)
Find the year when Yuto sells the hive.
[4]
www.seprodstore.com
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