The best replacement for exponential growth is logistic growth.

The best alternatives to exponential growth are rated as following:
★★★★★  logistic growth
★★★★  exponential decay
★★★★  linear growth
★★★★  geometric growth
★★  linear
★★  logarithmic growth
★  arithmetic growth
★  compound growth
★  logistic
★  factorial
★  compound interest
  polynomial growth
  logistical growth

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Speaking about exponential growth, one probably shouldn't forget about initial population.

Other search terms related to exponential growth and their ratings are:
★★★★★ initial population
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exponential growth
logistic growth
exponential decay