AP Calculus BC · Question of the Day

AP Calculus BC Question of the Day

A fresh daily question to build accuracy, reinforce recall, and turn practice into a steady habit.

Monday, September 21, 2026

A plant population satisfies $\frac{dy}{dt}=0.6y\left(1-\frac{y}{900}\right)$ . Which best describes the long-term limiting population?

Keep practicing AP Calculus BC

Question of the Day

Answer today's AP Calculus BC question, reveal the full explanation, then keep the streak going with a new question every day.

A plant population satisfies $\frac{dy}{dt}=0.6y\left(1-\frac{y}{900}\right)$ . Which best describes the long-term limiting population?

$0.6$
$900$ (correct answer)
$540$
$1/900$
No limit; it grows without bound

Explanation: This question tests logistic model reasoning by describing the long-term population limit. The carrying capacity $K=900$ is the value that $y$ approaches as $t$ increases, representing environmental sustainability. The inflection point at $y=450$ indicates where growth peaks before decelerating toward $K$ . In logistic models, for positive initial $y$ , solutions converge to $K$ , not exceeding it indefinitely. A tempting distractor like choice E fails because growth is bounded by $K$ , not unbounded. A transferable strategy for logistic models is to extract $K$ from the equation as the long-term limit, applicable for predicting asymptotic behavior in population dynamics.