Two Decays and Ten Steps | IB Math AI HL May 2025 Paper 2 Q6

Two exponential modes describe one coupled system. Find the exact solution, interpret the negative dip and long-run behaviour, then update both state variables through ten Euler steps in this complete 21-mark question. Source question: May 2025 IB Mathematics AI HL, Paper 2, Question 6 (21 marks). Paper code: 2225-7312. Pause at the question, try it yourself, then follow the complete explanation. English subtitles are available. CHAPTERS 00:00 A dip, a limit and ten numerical steps 00:29 (a) Two quantities form one state 01:00 (a) Find the two decay rates 01:32 (a) Two independent modes give the general solution 02:04 (b)(i) Let the initial state choose the amplitudes 02:37 (b)(i) Cancellation, then a negative dip 03:09 (b)(ii) Start with the required interval and slope 03:39 (b)(ii) / (c)(i) The derivative finds the dip 04:11 (b)(ii) Complete the concavity and asymptote 04:46 (c)(i) Buy at the minimum change 05:19 (c)(ii) An upper limit, approached over time 05:53 (d) A new equation needs a new calculation 06:24 (d) Update both components from one old state 07:01 (d) Ten linked state updates reach one minute 07:40 Six answers, one complete model question Explore IBvia learning resources and expert support: https://ibvia.com/ IBvia is an independent educational provider and is not affiliated with or endorsed by the International Baccalaureate Organization. #IBMath #Mathematics #IBvia