Analysis and Approaches for IBDP Maths Ebook 1 | Page 310

Your Practice Set – Analysis and Approaches for IBDP Mathematics
2. A farm food supplier monitors the number of chickens kept x against the monthly
consumption of chicken food ( y kg). The data for seven small farms on 1 July 2018 is
shown in the following table.
Number of chickens ( x ) 10 12 14 17 19 21 25
Monthly consumption ( y kg) 32 40 38 50 58 58 71
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 exact value of a and of b .
[4]
(b) Use the regression line to estimate the monthly consumption of chicken food
when there are 24 chickens in a farm, giving your answer to the nearest kg.
[3]
Starting from 1 July 2018, the monthly consumption of chicken food from the farm in (b)
increased by 5% each month.
(c) Calculate the monthly consumption of chicken food from the farm after half a
year.
[4]
The supplier will enlarge the size of the farm when its monthly honey production reaches
100 kg.
(d)
Find the year and the month when the supplier enlarges the size of the farm.
[4]
3. An environmental group records the numbers of wolves w and foxes f in a wildlife
reserve after t years, starting on 1 January 1981 as shown in the following table.
Number of years ( t ) 4 8 13 18
Number of wolves ( w ) 257 278 382 441
The relationship between the variables is modelled by the regression line with equation
w at b � � .
(a) (i) Find the correlation coefficient.
(ii) Write down the exact value of a and of b .
(b) Use the regression line to estimate the number of wolves on 1 January 1992,
giving your answer to the nearest integer.
Let f be the number of foxes in the reserve after t years, starting on 1 January 1981.
The number of foxes can be modelled by the equation
constant.
f
0.01kt
�50( e � 2) , where k is a
[4]
[3]
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