Final answer:
After the tenth interaction in a limited population of 20 people, the rate of increase in the number of infected individuals would become slower because the scenario is similar to the saturation point in enzyme kinetics. Once maximum capacity is reached, the rate no longer increases despite an increase in the number of potential hosts.
Step-by-step explanation:
Understanding the Rate of Infection in a Population
Keeping in mind the principles of exponential growth and the concept of saturation, as seen in enzyme interactions with substrates, the rate of increase would typically slow down once a certain threshold is reached. This phenomenon is akin to an enzyme saturation where, analogous to taxis at a taxi stand, once the maximum capacity is reached, the rate no longer increases despite an increase in the number of people (or in this case, substrates).
Exponential growth in biological populations means the growth rate—the number of organisms added in each reproductive generation—is itself increasing. However, as resources become limited or the population reaches a saturation point, the growth rate will slow, leading to a logistic growth curve rather than an exponential one. Similarly, in an infection scenario within a limited population, after a point, most or all individuals would be infected, so the rate of new infections would necessarily slow down as there would be fewer people left to infect.
The inclusion of real-life parameters, such as a twenty-person lab or a one-liter jar for bacteria, illustrates the principles of population dynamics and the limits of growth that can be imposed by environmental constraints or, in this example, the limited number of susceptible individuals.