The formula
$$P = 6800 \times 1.045^n$$
is used to predict the population, $P$, of an island $n$ years after 2018 - OCR - GCSE Maths - Question 16 - 2021 - Paper 1
Question 16
The formula
$$P = 6800 \times 1.045^n$$
is used to predict the population, $P$, of an island $n$ years after 2018.
(a) Write down the population of the island in 2... show full transcript
Worked Solution & Example Answer:The formula
$$P = 6800 \times 1.045^n$$
is used to predict the population, $P$, of an island $n$ years after 2018 - OCR - GCSE Maths - Question 16 - 2021 - Paper 1
Step 1
Write down the population of the island in 2018.
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Answer
To find the population in 2018, we set n=0 in the formula. Thus, the population is:
P=6800×1.0450=6800×1=6800.
Therefore, the population of the island in 2018 is 6800.
Step 2
Write down the percentage growth rate used in the formula.
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Answer
The formula uses a growth factor of 1.045. To find the percentage growth rate, we take 1.045−1=0.045, which translates to a growth rate of 4.5%.
Step 3
Work out the population predicted by the formula for the year 2030.
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Answer
For the year 2030, n=12 (as it is 12 years after 2018). Utilizing the given formula:
P=6800×1.04512.
Calculating this,
P≈6800×1.601=10885.68.
Thus, the predicted population for the year 2030 is approximately 10886.
Step 4
Give one reason why the answer to (c)(i) may not be reliable.
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Answer
The prediction may not be reliable because it assumes that the growth rate will remain constant over the years, which may not reflect real-world changes such as economic, environmental, or social factors affecting the population.
