CAIE A-Level Mathematics 2.2.4 Linearising Relationships

Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise transforming power or exponential relationships into straight-line form and interpreting gradient and intercept.

How this is tested

take logarithms and rearrange the relationship into a straight-line equation
match transformed variables to Y=mX+c and identify the gradient and intercept
use two graph points to calculate constants, then reverse logarithms where required

[Maximum number: 3]

The variables x and y satisfy the equation $A y=b^{x}$ , where A and b are constants.

When $x=3.4, \ln y=0.86$ and when $x=5.7, \ln y=2.56$ .

Find the value of A and the value of b. Give your answers correct to 2 significant figures.