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Date May Example question Marks available 1 Reference code EXM.1.AHL.TZ0.21
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Explain Question number 21 Adapted from N/A

Question

Saloni wants to find a model for the temperature of a bottle of water after she removes it from the fridge. She uses a temperature probe to record the temperature of the water, every 5 minutes.

After graphing the data, Saloni believes a suitable model will be

T = 28 a b t , where  a , b R + .

Explain why 28 T can be modeled by an exponential function.

[1]
a.

Find the equation of the least squares exponential regression curve for  28 T .

[3]
b.

Write down the coefficient of determination,  R 2 .

[1]
c.i.

Interpret what the value of R 2  tells you about the model.

[1]
c.ii.

Hence predict the temperature of the water after 3 minutes.

[2]
d.

Markscheme

Rearranging the model gives 28 T = a b t        A1

So  28 T can be modeled by an exponential function.        AG

[2 marks]

a.

       (A1)

28 T = 22.7 ( 0.925 ) t         M1A1

[3 marks]

b.

R 2 = 0.974          A1

[1 mark]

c.i.

Since the value of R 2  is close to +1, the model is a good fit for the data.         R1

[1 mark]

c.ii.

T = 28 ( 22.69 ) ( 0.9250 ) 3 = 10.0  minutes         M1A1

[2 marks]

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.i.
[N/A]
c.ii.
[N/A]
d.

Syllabus sections

Topic 4—Statistics and probability » AHL 4.13—Non-linear regression
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Topic 4—Statistics and probability

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