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Date May Example question Marks available 3 Reference code EXM.1.AHL.TZ0.15
Level Additional Higher Level Paper Paper 1 Time zone Time zone 0
Command term Hence and Find Question number 15 Adapted from N/A

Question

Adesh wants to model the cooling of a metal rod. He heats the rod and records its temperature as it cools.

He believes the temperature can be modeled by T(t)=aebt+25, where a,bR.

Hence

Show that ln(T25)=bt+lna.

[2]
a.

Find the equation of the regression line of ln(T25) on t.

[3]
b.

find the value of a and of b.

[3]
c.i.

predict the temperature of the metal rod after 3 minutes.

[2]
c.ii.

Markscheme

ln(T25)=ln(aebt)       M1

ln(T25)=lna+ln(ebt)            A1

ln(T25)=bt+lna            AG

[2 marks]

a.

ln(T25)=0.00870t+3.89      M1A1A1

[3 marks]

b.

b=0.00870       A1

a=e3.89...=49.1     M1A1

[3 marks]

c.i.

T(180)=49.1e0.00870(180)+25=35.2    M1A1

[2 marks]

c.ii.

Examiners report

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

Syllabus sections

Topic 4—Statistics and probability » SL 4.4—Pearsons, scatter diagrams, eqn of y on x
Show 146 related questions
Topic 2—Functions » AHL 2.10—Scaling large numbers, log-log graphs
Topic 2—Functions
Topic 4—Statistics and probability

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