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Date	May Example question	Marks available	7	Reference code	EXM.1.AHL.TZ0.14
Level	Additional Higher Level	Paper	Paper 1	Time zone	Time zone 0
Command term	Find	Question number	14	Adapted from	N/A

Question

It is believed that two variables, $v$ and $w$ are related by the equation $v = k{w^n}$ , where $k{\text{,}}\,\,n \in \mathbb{R}$ . Experimental values of $v$ and $w$ are obtained. A graph of ${\text{ln}}\,v$ against ${\text{ln}}\,w$ shows a straight line passing through (−1.7, 4.3) and (7.1, 17.5).

Find the value of $k$ and of $n$ .

Markscheme

${\text{ln}}\,v = n\,{\text{ln}}\,w + {\text{ln}}\,k$ M1A1

gradient $= \frac{{17.5 - 4.3}}{{7.1 + 1.7}}{\text{ }}\left( { = 1.5} \right)$ M1

$n = 1.5$ A1

$y$ -intercept $= 1.5 \times 1.7 + 4.3{\text{ }}\left( { = 6.85} \right)$ M1

$k = {e^{6.85}} = 944$ M1A1

[7 marks]

Examiners report

[N/A]

Syllabus sections

Topic 2—Functions » AHL 2.10—Scaling large numbers, log-log graphs

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