At the start of 2018, the population of a town was 17,150 - OCR - GCSE Maths - Question 22 - 2019 - Paper 6

Using the population at the start of 2019, we have:

$P = a r^t$

At $t = 1$ (start of 2019):

$16,807 = 17,150 imes r^1$

Rearranging gives:

$r = \frac{16,807}{17,150} \approx 0.98$

To evaluate the population at the start of 2022, we need to calculate for $t = 4$:

$P = 17,150 imes (0.98)^4$

Calculating this:

$P \approx 17,150 \times 0.92236816 \approx 15,818.12$

Thus, the predicted population at the start of 2022 is approximately 15,818, which is indeed less than 16,000.

For the start of 2017, we set $t = -1$:

$P = 17,150 \times (0.98)^{-1}$

Calculating this gives:

$P \approx 17,150 \times 1.02040816 \approx 17,500.99$

Therefore, the population at the start of 2017 might have been approximately 17,501.