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π π π π=πβ(1β π 2πβ1)= π πΎ πβ1 =π π π‘π β π‘πβ1 π π+π π ln(ππ ) ln( π ) π πβ1 π =ππ π‘π β π‘πβ1 (3.3) π refers to the user population at the time i. Discrete growth rate model can be fitted into the continuous one, as proposed in prior studies by Cauwels and Sornette: π Where π π depicts discrete growth rate, i represents the point in time, t refers to the time period, and (3.4) Expressing equation (3.3) as a linear function π¦ = ππ₯ + π, y and x can be represented in terms of discrete growth rate, π π, and user population from different time, π + π : π π πβ1 π = π πΎ=βπ π We can then express r and K accordingly, π¦ = π π π (3.5) π₯=π+π (3.6) π πβ1 When plotting the time-series data of Douyinβs user population along with its linear regression, we would obtain its discrete growth rate as a linear function in form of π¦ = ππ₯ + π, thus obtaining values of a and b. From there we could calculate, under equation (3.7) and (3.8), to get the values of r and K. - 19 - (3.7) (3.8)PDF Image | Analysis of ByteDance with a close look on Douyin TikTok
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