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Precalculus · FRQ Trainer

Free-response 1 of 24 · Exponential & Logarithmic Functions

6 pts our rubric

The real Precalculus Section II is 4 free-response questions in 70 minutes, 37.5% of your score. Four 6-point questions. Part A (35 minutes, graphing calculator): function concepts and modeling a non-periodic context. Part B (35 minutes, no calculator): modeling a periodic context and symbolic manipulations. This prompt is ours, written to the same skills — score it against the rubric below, not against that structure.

Prompt

The population of a species of fish in a lake is modeled by the logistic function P(t) = 1200 / (1 + 15e^(-0.2t)), where t is the number of years since the lake was stocked.

aDetermine the initial population of the fish.2 pts

bFind the carrying capacity of the lake for this species.2 pts

cAt what time t is the population growing the fastest?2 pts

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Write your response first — then grade it with AI or self-score against the rubric.