In Example 4.4.6 of Bob's Bee Hive, we observed that the minimum capacity was 2 (thousands) and the maximum capacity was 8 (thousands). The constant of proportionality was k = 0.25.

Now let's assume that the minimum capacity is 4 (thousands) and the maximum capacity is 20 (thousands) with the constant of proportionality still at k = 0.25. If the bee population is initially 7 (thousands), so P (0) = 7, then calculate the bee population in 2 years, so calculate P (2).

So here you must:

1. Write the new differential equation for this model. 2. Separate the variables and solve the DE with IC P (0) = 7. 3. Calculate P (2). 4. Give your answer with 4 decimal places of precision!