3.30: Linear law: $\ln y$ against $\ln x$ for $y=Ax^{b}$

0606/13/M/J/23 — Question 7 · 10 marks

(a)

The table shows values of

x

and

y

related by

y=Ax^{b}

x

1.5

2

2.5

3

4

|
|

y

13.8

27.5

46.9

72.6

145

Use the data to draw a straight line graph of

\ln y

against

\ln x

[3]

(b)

Use your graph to estimate the values of

A

and

b

[5]

(c)

Estimate the value of

x

when

y=100

[2]

3.30: Linear law: ln⁡y\ln ylny against ln⁡x\ln xlnx for y=Axby=Ax^{b}y=Axb