Apps. and Interpretation for IBDP Maths Ebook 1 | Page 339

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
� � , where k is a
0.01kt
50( e 2)
[4]
[3]
(c) After ten years, there were 930 foxes in the reserve. Find k .
[3]
(d) During which year were the number of wolves the same as the number of foxes?
[4]
4. A health clinic counted the number of breaths per minute u and the number of pulse
beats per minute v for a patient t minutes after his 10 km race, as shown in the following
table.
22
Number of minutes ( t ) 1 3 5 6 7
Number of breaths per minute (u ) 58 55 53 50 52
The relationship between the variables is modelled by the regression line with equation
u at b � � .
(a) (i) Find the correlation coefficient.
(b)
(ii) Write down the exact value of a and of b .
[4]
Use the regression line to estimate the number of breaths per minute 12 minutes
after the race, giving your answer to the nearest integer.
[3]
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