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The number of animals in a population at the start of year i is $P_i$ - Edexcel - GCSE Maths - Question 14 - 2018 - Paper 3

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The number of animals in a population at the start of year i is $P_i$. The number of animals at the start of year 1 is 400. Given that $P_{n+1} = 1.01 P_n$, work out... show full transcript

Worked Solution & Example Answer:The number of animals in a population at the start of year i is $P_i$ - Edexcel - GCSE Maths - Question 14 - 2018 - Paper 3

Step 1

Calculate the number of animals at the start of year 2

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Answer

Using the formula Pn+1=1.01PnP_{n+1} = 1.01 P_n, we can calculate the number of animals at the start of year 2 as follows:

P2=1.01P1P_2 = 1.01 P_1

Substituting the known value:

P2=1.01×400=404.P_2 = 1.01 \times 400 = 404.

Step 2

Calculate the number of animals at the start of year 3

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Answer

Next, we apply the formula again for year 3:

P3=1.01P2P_3 = 1.01 P_2

Substituting the value we just computed:

P3=1.01×404=408.04.P_3 = 1.01 \times 404 = 408.04.

Since the number of animals must be a whole number, we can round to the nearest whole number, which gives:

P3≈408.P_3 \approx 408.

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