Population 2021 and 2026, arithmetic and decreasing rate

Census interval 10 years; last census 2011. For 2021, $n = 1$ decade; for 2026, $n = 1.5$ decades.

Population in 2021 (n = 1)

Arithmetical increase method

Average increase per decade: $\bar x = \dfrac{83{,}000-18{,}000}{5} = 13{,}000.0$

$$P_{2021} = P_n + n\bar x = 83{,}000 + 1\times 13{,}000.0 = 96{,}000$$

Decreasing rate of growth method

Average decrease in rate $= 6.061\%$ per decade.

$P_{2021} = 99{,}348$

Population in 2026 (n = 1.5)

Arithmetical increase method

Average increase per decade: $\bar x = \dfrac{83{,}000-18{,}000}{5} = 13{,}000.0$

$$P_{2026} = P_n + n\bar x = 83{,}000 + 1.5\times 13{,}000.0 = 102{,}500$$

Decreasing rate of growth method

Average decrease in rate $= 6.061\%$ per decade.

Population at 2026 is obtained by linear interpolation between the decade values: $P_{2026} = 106{,}122$.

Summary

Answer: Arithmetic increase: 2021 = 96,000, 2026 = 102,500. Decreased rate of growth: 2021 = 99,348, 2026 = 106,122.