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The number of rabbits on a farm at the end of month n is P - Edexcel - GCSE Maths - Question 23 - 2019 - Paper 2
Question 23
The number of rabbits on a farm at the end of month n is P. The number of rabbits at the end of the next month is given by $P_{n+1} = 1.2P_n - 50$ At the end of Marc... show full transcript
Worked Solution & Example Answer:The number of rabbits on a farm at the end of month n is P - Edexcel - GCSE Maths - Question 23 - 2019 - Paper 2
Step 1
Considering your results in part (a), suggest what will happen to the number of rabbits on the farm after a long time.
Answer
Considering the recursive relationship established in part (a), the number of rabbits tends to decrease over time even as the formula suggests an initial growth. The negative constant (-50) denotes that for every cycle (month), a significant number of rabbits are removed.
Over the long term, the rabbit population will stabilize, but it is likely that there will be no rabbits left as the population continues to shrink. Thus, we can conclude that after a long time, there will eventually be fewer rabbits or possibly no rabbits left on the farm.