Population 2021 and 2028, incremental method

The census interval is 10 years and the last census is 1991. For 2021, $n = 3.0$ decades; for 2028, $n = 3.7$ decades. "Changing rate of increase" is taken as the decreasing (changing) rate of growth method.

Population in 2021 (n = 3.0)

Incremental increase method

Increase per decade: 2,000, 3,000, 2,500, 6,600, 7,400, 5,550, 7,450, 6,500; incremental increase: 1,000, -500, 4,100, 800, -1,850, 1,900, -950. $\bar x = 5{,}125.00$, $\bar y = 642.86$

$$P_{2021} = P_n + n\bar x + \frac{n(n+1)}{2}\bar y = 61{,}000 + 3(5{,}125.00) + \frac{3(4)}{2}(642.86) = 80{,}232$$

Decreasing rate of growth method

Average decrease in rate $= -0.275\%$ per decade.

$P_{2021} = 86{,}800$

Population in 2028 (n = 3.7)

Incremental increase method

Increase per decade: 2,000, 3,000, 2,500, 6,600, 7,400, 5,550, 7,450, 6,500; incremental increase: 1,000, -500, 4,100, 800, -1,850, 1,900, -950. $\bar x = 5{,}125.00$, $\bar y = 642.86$

$$P_{2028} = P_n + n\bar x + \frac{n(n+1)}{2}\bar y = 61{,}000 + 3.7(5{,}125.00) + \frac{3.7(4.7)}{2}(642.86) = 85{,}552$$

Decreasing rate of growth method

Average decrease in rate $= -0.275\%$ per decade.

Population at 2028 is obtained by linear interpolation between the decade values: $P_{2028} = 94{,}715$.

Summary

Answer: Incremental increase: 2021 = 80,232, 2028 = 85,552. Changing rate of increase: 2021 = 86,800, 2028 = 94,715.