A biologist is running some experiments on a culture of bacteria.
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A biologist is running some experiments on a culture of bacteria. She puts the culture in a petri dish and notes that initially, the population increases rapidly. But soon it approaches a steady state. Which of the following graphs best represents the population P, as a function of time T?
Show answer & explanation
Logistic growth models a population that initially increases rapidly (exponentially) and then levels off asymptotically as it approaches environmental carrying capacity (steady state).
Step-by-step Derivation:
Step 1: Exponential growth increases without bound.
Step 2: When resources become limiting, the growth rate slows and approaches a steady-state asymptote (carrying capacity K).
Step 3: This characteristic sigmoidal (S-shaped) behavior is modeled by the logistic equation dP/dt = rP(1 - P/K).