1. Write a differential equation describing the following situation:

The rate at which people become involved in a corporate bribing scheme is jointly proportional to the number of people already involved and the number of people who are not yet involved. Suppose there are a total of 6000 people in the company. Use k for the constant, P for the number of people who are involved in the scheme, and t for time.

dP/dt = k * (600 - P) * P

Step-by-step explanation:

Given:

- Total number of people in company N = 6000

- Total people involved in bribery P

The rate at which people become involved in a corporate bribing scheme is jointly proportional to the number of people already involved and the number of people who are not yet involved.

Find:

Write a differential equation

Solution:

- The following differential equation can be used to describe the situation above:

Number of people not affected = N - P

- Hence we can write a differential equation:

dP / dt = k * (N - P) * P

- input the value of N:

dP/dt = k * (600 - P) * P