Practice question · Multiple choice
Exponential growth and logistic growth agree closely at first and diverge completely later. What in the equation causes the split?
Hints
- Look at the logistic equation's extra factor. What is its value when the population is tiny?
- Ask what happens to that factor as the population approaches K.
Show the answer
C. The logistic growth rate falls near a carrying capacity
Why
The (1 − N/K) factor is nearly 1 when N is small and heads to zero near the ceiling, so the two models are indistinguishable exactly when a startup is fitting its curve. That is why early growth is such weak evidence about which regime you are in.
Practise Differential Equations
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