2.3: Linear law graph: $\ln y$ against $\ln x$

0606/21/M/J/18 — Question 8 · 7 marks

An experiment was carried out recording values of

y

for certain values of

x

. The variables

x

and

y

are thought to be connected by the relationship

y = ax^{n}

, where

a

and

n

are constants.

The values of

\ln y

and

\ln x

were plotted and a line of best fit drawn. This is shown in the diagram below.

(i)

Transform the relationship

y = ax^{n}

into straight line form.

[2]

(ii)

Use the graph to find the value of

a

and of

n

, stating the coordinates of the points that you use.

[3]

(iii)

Find the value of

x

when

y = 50

[2]

2.3: Linear law graph: ln⁡y\ln ylny against ln⁡x\ln xlnx