Q.A population of Paramoecium caudatum was grown in a culture medium. After 5 days the culture medium became overcrowed with Paramoeium and had depleted nutrients. What will happen to the population and what type of growth curve will the population attain? Draw the growth curve.

When nutrients run out and space becomes limited, the population of Paramoecium caudatum stops growing exponentially. The number of individuals first stabilises at the carrying capacity of the culture medium, then begins to decline as deaths exceed births due to starvation and waste accumulation. This pattern produces an S-shaped or sigmoid growth curve, not a J-shaped one. …

In a closed culture medium—like the one described—resources are finite. Initially, with plenty of food and space, the Paramecium caudatum population grows rapidly, doubling at a constant rate. This is the exponential or logarithmic phase, where each individual reproduces and adds to the population without constraint. The curve during this period is J-shaped, steeply rising.

But after five days, the culture becomes overcrowded. Nutrients are depleted, and waste products accumulate. The environment can no longer support the same rate of reproduction. Death rates begin to rise, and birth rates fall. The population stops increasing and enters a stationary phase, where the number of individuals remains roughly constant. This plateau reflects the carrying capacity of the culture—the maximum population size the medium can sustain.

The type of growth curve the population attains is called a logistic growth curve, also known as an S-shaped or sigmoid curve. It starts with a slow initial increase (lag phase), accelerates into exponential growth (log phase), then slows and finally levels off at the carrying capacity. …

Track resource availability over time as the deciding variable: falling nutrients plus rising density is exactly the condition that turns $dN/dt = rN$ into $dN/dt = rN(K-N)/K$, so the curve must …