Question 6 A fish farm operates a fish breeding pond in which the population of a particular fish increases by 3% per month. (a) Give the recurrence formula to calculate the fish population at the end of each month, assuming the rate does not change and the initial population is 1000 fish. Solution Item* Behaviours Marks (S/C) Defines the recurrence relationship 1 simple States 1 simple (b) Calculate the population numbers at the end of the first six months of its operation, given the initial population is 1000 fish. Solution Item* Behaviours Marks (S/C) Starts the sequence at P1 = 1030 1 simple Completes the sequence at P6=1194 1 simple (c) After the initial six months, 40 fish per month are removed at the end of each month. Assuming the population growth is maintained at 3%, how many fish are expected to be in the tank at the end of 12 months? Solution Item* Behaviours Marks (S/C) States the new recurrence relation 1 complex Q0 States the initial condition 1 complex Calculates the correct population 1 complex (d) Describe what is happening to the population. Solution The population of fish is declining slowly.
Question 6 A fish farm operates a fish breeding pond in which the population of a particular fish increases by 3% per month. (a) Give the recurrence formula to calculate the fish population at the end of each month, assuming the rate does not change and the initial population is 1000 fish. Solution Behaviours Marks Item* (S/C) Defines the recurrence relationship States 1 1 simple simple (b) Calculate the population numbers at the end of the first six months of its operation, given the initial population is 1000 fish. Solution Behaviours Marks Item* (S/C) Starts the sequence at P1 = 1030 Completes the sequence at P6=1194 1 1 simple simple (c) After the initial six months, 40 fish per month are removed at the end of each month. Assuming the population growth is maintained at 3%, how many fish are expected to be in the tank at the end of 12 months? Solution Behaviours Marks Item* (S/C) States the new recurrence relation States the initial condition Q0 Calculates the correct population 1 1 1 complex complex complex (d) Describe what is happening to the population. Solution The population of fish is declining slowly.