= Solution
With the same low-density rate and carrying capacity, the two per-capita growth rates are
$$
\frac{\dot n}{n}=\alpha\left(1-\frac{n^2}{K^2}\right)
$$
for the cubic model and
$$
\frac{\dot n}{n}=\alpha\left(1-\frac nK\right)
$$
for logistic growth. The logistic correction is linear in a small population, whereas the cubic correction is quadratic. Consequently the cubic trajectory initially follows pure exponential growth more closely and lies above the logistic trajectory before both approach $K$. Plotting measured per-capita growth against $n$ distinguishes a linear decline from a curve with zero slope at the origin.
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