2. Recurrence Relations Pollution Problems

3. Q1. The initial quantity of pollution in the loch is 45 tons, the Council remove 36% during the week and a factory discharges 9 tons into the loch each Sunday. i) Find the amount of pollution after 1, 2, 3 and 4 weeks. ii) Establish a recurrence relation and hence find the long term state of the loch.

4. Repeat question 1 for examples 2-5 which follow. Q2. Initial quantity of pollution = 33 tons Council remove 35% per week during the week. Factory is allowed to discharge 20 tons per week at the end of the week.. Q3. Initial quantity of pollution = 40 tons Council remove 60% per week during the week Factory is allowed to discharge 15 tons per week at the end of the week.

5. Q4. Initial quantity of pollution = 16.5 tons Council remove 52% per week during the week Factory is allowed to discharge 6 tons per week at the end of the week. Q5. Initial quantity of pollution = 2000 tons Council remove 34% per week during the week Factory is allowed to discharge 45 tons per week at the end of the week.

6. Q6. Initial quantity of pollution = 380 tons Council remove 15% per week during the week for each of the first five weeks and then they must remove 20% per week after this period. Factory is allowed to discharge 20 tons per week at the end of the week. Q7. Initial quantity of pollution = 100 tons Council remove 35% per week during the week for each of the first four weeks and then they must remove 22% per week after this period. Factory is allowed to discharge 35 tons per week at the end of the week.

7. Q8. Initial quantity of pollution = 600 tons Council remove 45% per week during the week for each of the first three weeks; 35% per week during the week for each of the next four weeks and then they must remove 25% per week, every week, after this period. Factory is allowed to discharge 40 tons per week at the end of the week.