3.6: Linear law: $\ln y$ against $x^{2}$ for $y=Ab^{x^{2}}$

0606/12/F/M/23 — Question 5 · 11 marks

(a)

The table shows values of

x

and

y

related by

y=Ab^{x^{2}}

, where

A

and

b

are constants.

x

1

1.5

2

2.5

|
|

y

2.0

11.3

128

2896

Use the data to draw a straight line graph of

\ln y

against

x^{2}

[2]

(b)

Use your graph to estimate the values of

A

and

b

. Give your answers correct to

1

significant figure.

[5]

(c)

Estimate the value of

y

when

x=1.75

[2]

(d)

Estimate the positive value of

x

when

y=20

[2]

3.6: Linear law: ln⁡y\ln ylny against x2x^{2}x2 for y=Abx2y=Ab^{x^{2}}y=Abx2