A lift that decays all the way to zero

Question

A feature's weekly lift is fading: week 1 = 8%, week 2 = 4%, week 3 = 2%, week 4 = 1%. The team wants the durable long-run lift before deciding whether to ship.

Estimate the steady-state lift, and say what it implies for the ship decision.

Accepted Answer

Model: floor plus fading bonus. Write each week as 	ext{lift}t = L + A \cdot r^{\,t}, with L the durable lift and A \cdot r^{t} the shrinking novelty bonus. Find the ratio from the weekly drops. - Week 1 to 2: 8 	o 4, drop of 4. - Week 2 to 3: 4 	o 2, drop of 2. - Week 3 to 4: 2 	o 1, drop of 1. The drops (4, 2, 1) halve each week, so r = 1/2. Solve for the floor. Test L = 0: the excesses above zero are the lifts themselves, 8, 4, 2, 1, which halve perfectly. So the lift is converging to L = 0\%: the whole series is just a decaying bonus with nothing underneath. Interpretation and decisio…

A lift that decays all the way to zero

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