CAIE A-Level Mathematics 3.2.2 Exponential & ln

CAIE A-Level Mathematics 3.2.2 Exponential & ln
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise using e^x and ln x as inverse functions, reading exponential graph behaviour and solving for coordinates involving e^{kx}.

How this is tested

  • link e^x and ln x as inverse functions when finding coordinates on exponential graphs

Question 5(a)

[Maximum number: 2]
Figure for Question 5(a) — CAIE A-Level Mathematics

The diagram shows the curve with equation y=8e−12x−1y=8 \mathrm{e}^{-\frac{1}{2} x}-1. The curve meets the axes at the points A and B. The shaded region is bounded by the curve and the line segment AB.

Show that the x-coordinate of B is 6ln⁡26 \ln 2.