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 March there are 200 rabbits on the farm. (a) Work out how many rabbits there will be on the farm at the end of June. (b) Considering your results in part (a), suggest what will happen to the number of rabbits on the farm after a long time.

GCSE Edexcel Maths Algebraic Proof: The number of rabbits on a farm

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

Part (a) - Work out how many rabbits there will be on the farm at the end of June.

96%

114 rated

Answer

To find the number of rabbits at the end of June, we need to calculate the number of rabbits for each month starting from the end of March.

End of March (P_0): 200 rabbits.
End of April (P_1):

Using the formula: $P_{1} = 1.2P_{0} - 50$ $P_{1} = 1.2(200) - 50 = 240 - 50 = 190$
End of May (P_2):

Again using the formula: $P_{2} = 1.2P_{1} - 50$ $P_{2} = 1.2(190) - 50 = 228 - 50 = 178$
End of June (P_3):

Applying the formula once more: $P_{3} = 1.2P_{2} - 50$ $P_{3} = 1.2(178) - 50 = 213.6 - 50 = 163.6$

Therefore, rounding to the nearest whole number, there will be approximately 164 rabbits on the farm at the end of June.

Step 2

Part (b) - Considering your results in part (a), suggest what will happen to the number of rabbits on the farm after a long time.

99%

104 rated

Answer

Based on the calculation in part (a), the number of rabbits shows a decreasing trend. As seen, the population began with 200 rabbits and decreased to 164 by the end of June.

This suggests that eventually, the number of rabbits will continue to decrease due to the negative impact from the formula. After a long time, the population will stabilize at a lower number but will likely approach zero, leading to a conclusion that there will not be any rabbits left on the farm.

The number of rabbits on a farm at the end of month n is P - Edexcel - GCSE Maths - Question 23 - 2019 - Paper 2

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

Part (a) - Work out how many rabbits there will be on the farm at the end of June.

Part (b) - Considering your results in part (a), suggest what will happen to the number of rabbits on the farm after a long time.

Join the GCSE students using SimpleStudy...