Campus Rumor Spread

A rumor begins spreading on a campus of 2000 students. Initially, 5 students know the rumor. Each day, the number of students who have heard the rumor is recorded. The data shows initial exponential growth that slows as most students have already heard it.

Your tasks:

1. Identify the mathematical model that describes this growth pattern
2. Write the differential equation (ODE)
3. Provide the analytical solution
4. Estimate the model parameters from the data (K, r, P₀)
5. Predict: how many days until 90% of students (1800) have heard the rumor?