Suppose a rumor is going around a group of 210 people. Initially, only 34 members of the group have heard the rumor, but 3 days later 69 people have heard it. Using a logistic growth model, how many people are expected to have heard the rumor after 6 days total have passed since it was initially spread? (Round your answer to the nearest whole person.)

116 people are expected to have heard the rumor after 6 days total have passed since it was initially spread.

Step-by-step explanation:

Logistic function:

The logistic function is given by:

In which:

Considering that K is the carrying capacity, k is the growth/decay rate and P(0) is the initial population.

Suppose a rumor is going around a group of 210 people.

This means that

Initially, only 34 members of the group have heard the rumor:

This means that and:

So

3 days later 69 people have heard it.

This means that , and we use this to find k.

So

How many people are expected to have heard the rumor after 6 days total have passed since it was initially spread?

This is P(6), so:

116 people are expected to have heard the rumor after 6 days total have passed since it was initially spread.