APFIVE The number of native species in a region, $$N(x)$$, is modeled by the polynomial $$N(x) = -x^3 + 12x^2 - 35x + 50$$, where $$x$$ represents the number of years since an invasive species was introduced. Which of the following conclusions is best supported by this model?
The turning points in the polynomial reveal that the introduction of the invasive species has an immediate and uniformly positive effect on biodiversity, leading to a continuous increase in native species counts.
The polynomial suggests that while there are short-term fluctuations in native species populations, the overall trend is one of exponential growth in native species numbers, even in the presence of an invasive species.
The analysis of the polynomial’s turning points suggests that there may be periods of temporary recovery in native species counts, but the overall negative cubic term implies a long-term decline in biodiversity as a result of the invasive species’ impact.
The existence of local extrema in the model indicates that the invasive species causes the native species count to remain constant over time with no significant fluctuations.
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