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IB Maths AI HL Ahl 2 10 Hl Logarithmic Scaling and Linearization Questions

Practise IB Mathematics HL 2.10 by applying logarithmic scaling and linearization methods to questions from the Question Bank.

Syllabus
First assessment 2021
Course
Mathematics: applications and interpretation HL
Level
HL

Exam points

  • Transform exponential or power data with logarithms to obtain a linear relationship and choose the appropriate axes.
  • Derive and interpret the gradient and intercept of the linearised graph, then convert them back to the original model parameters.
  • Use the fitted relationship to scale or predict values and assess the validity of the linearisation and its domain.

IB Maths AI HL Ahl 2 10 Hl Logarithmic Scaling and Linearization Questions question 1

[Maximum number: 5]

A student investigating the relationship between chemical reactions and temperature finds the Arrhenius equation on the internet.

k=Ae−cTk=A \mathrm{e}^{-\frac{c}{T}}

This equation links a variable k with the temperature T, where A and c are positive constants and T>0.

Question (a)

(a)

The Arrhenius equation predicts that the graph of ln⁡k\ln k against 1T\frac1T is a straight line.
Write down

[ 2 ]

Question (i)

(i)

the gradient of this line in terms of c;

[ 1 ]

Question (ii)

(ii)

the y-intercept of this line in terms of A.

[ 1 ]

Question (b)

(b)

Find an estimate of

[ 3 ]

Question (i)

(i)

c;

[ 1 ]

Question (ii)

(ii)

A.

It is not required to state units for these values.

[ 2 ]
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