Question

In a building with 70 residents, a rumor spreads through a diffusion process. At what point is the rate of diffusion greater: when 15 people have heard, or when 50 people have heard? (Hint: you can solve this with only a small amount of math)

Answer 1

The rate of diffusion of a rumor is typically greater when fewer people have heard it. Therefore, in a building with 70 residents, the diffusion rate is greater when only 15 people have heard the rumor as opposed to when 50 people have heard it, because more people are available to spread the rumor to.

Step-by-step explanation:

When considering the rate of diffusion of a rumor in a building with 70 residents, we need to understand at which point the rate is greater - when 15 people have heard it or when 50 have heard it.

Diffusion processes can often be compared to an enzyme-substrate reaction as per the given analogy. With a finite number of individuals who have yet to hear the rumor (akin to enzyme molecules), there is a point at which nearly everyone capable of hearing and spreading the rumor (the substrate in our analogy) will already know it, leading to a diminished rate of further spread since fewer people are left to tell it to.

Therefore, the rate of diffusion is typically greater when there are more people who have not heard the rumor. Hence, when 15 people have heard the rumor, the rate of diffusion is likely greater than when 50 people have heard it, because more potential individuals can still learn of the rumor from the 55 who have not heard it.