A faster decay (ratio one-third) toward 1 percent

Question

A feature's weekly lift decays quickly as novelty fades: week 1 = 10%, week 2 = 4%, week 3 = 2%, week 4 = 1.33%. The team wants the durable long-run lift.

Estimate the steady-state lift this is converging to.

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. Here the decay looks faster than a simple halving, so expect a smaller ratio. Find the ratio from the weekly drops. - Week 1 to 2: 10 	o 4, drop of 6. - Week 2 to 3: 4 	o 2, drop of 2. - Week 3 to 4: 2 	o 1.33, drop of about 0.67. Each drop is one-third of the previous (6, 2, 0.67), so r = 1/3. Solve for the floor. The excess above L should shrink by a factor of 1/3 each week. Test L = 1: the excesses are 10-1, 4-1, 2-1, 1.33-1 = 9, 3…

A faster decay (ratio one-third) toward 1 percent

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