Logistic growth · free viral adoption · daily resolution

The exponential curve
with a ceiling

Self-reinforcing, free viral growth: no acquisition spend, just network effects rocketing the user count almost vertically — until the carrying capacity (the total addressable market) bends it into a plateau. Adjust the viral rate, price and every cost; the steeper the free growth, the sooner it slams into the ceiling. The horizontal axis is time (days).

Fixed parameters

The launch metrics and the market ceiling. Growth is free and viral — there is no per-user acquisition cost here.

Initial users (launch) N₀

Carrying capacity (ceiling K) users / TAM

Play with these

A higher viral rate makes the free growth extremely steep. Price minus cost per user decides whether that explosion earns or burns.

Viral growth rate (r) 12%/day

Subscription price / user $3/month

Variable cost / user $1/month

Fixed cost $150k/month

Initial investment $2Menter in $K

All costs live here: a per-user serving cost (scales with the explosion) plus a fixed monthly cost. There is no acquisition cost because the growth is free.

Inflection day (max velocity)

—

Inflection size (K/2)

—

Margin / user (price − cost)

—

Break-even day

—

Users (the exponential rocket) Ceiling K · inflection Cumulative cash Monthly revenue (run-rate)

Users: N(t) = K / (1 + ((K−N₀)/N₀)·e^(−r·t)) · Inflection: t = (1/r)·ln((K−N₀)/N₀) at N = K/2
Revenue: R(t) = price·N(t) (monthly run-rate) · Cashflow: π = (price − varCost)·N(t) − fixed per month · Cash: C(t) = investment + Σ(π/30)