A laboratory population of yeast is observed to grow in a limited nutrient medium. The population initially shows a lag phase, followed by phases of acceleration and deceleration, and finally reaches an asymptote when the population density reaches the carrying capacity of the medium. Which of the following equations correctly models this specific pattern of growth?

Step-by-step solution

The growth pattern described (a lag phase, phases of acceleration and deceleration, and an asymptote at carrying capacity) is characteristic of a sigmoid (S-shaped) growth curve. This type of population growth is called Verhulst-Pearl Logistic Growth, which occurs when resources are limited. The differential equation representing this growth model is d N d t = r N ( K-N K ) , where N is population density at time t , r is the intrinsic rate of natural increase, and K is the carrying capacity. The equations d N d t