जनसङ्ख्या अध्ययनका लागि सामान्य सङ्ख्यात्मक विधि

Given: Elderly population in 2001, $P_0 = 28{,}550$; in 2011, $P_t = 35{,}420$; time $t = 2011 - 2001 = 10$ years.

Formula (exponential growth method):

$P_t = P_0 e^{rt} \quad\Rightarrow\quad r = \frac{\ln(P_t / P_0)}{t}$

Calculation:

$\frac{P_t}{P_0} = \frac{35{,}420}{28{,}550} = 1.2406$

$\ln(1.2406) = 0.2156$

$r = \frac{0.2156}{10} = 0.02156$

In percentage, $r = 0.02156 \times 100 \approx 2.16\%$.

Result: The annual exponential growth rate of the elderly population of the district during 2001-2011 is about 2.16% per year.

The formula for estimating population-doubling time is:

$T_d = \frac{70}{r}$

where $T_d$ is the doubling time in years and $r$ is the annual population growth rate in percent.

Using the rule of 70:

$T_d = \frac{70}{1.35} \approx 51.85 \approx 52 \text{ years}$

So Nepal's population would double in about 52 years at the 2011 growth rate of 1.35%.

Given: $P_0 = 23{,}151{,}523$ (2001), $P_t = 26{,}494{,}504$ (2011), $t = 2011-2001 = 10$ years.

Formula (exponential growth method):

$P_t = P_0 e^{rt} \quad\Rightarrow\quad r = \frac{\ln(P_t/P_0)}{t}$

Calculation:

$\frac{P_t}{P_0} = \frac{26{,}494{,}504}{23{,}151{,}523} = 1.1444$

$\ln(1.1444) = 0.1349$

$r = \frac{0.1349}{10} = 0.01349$

Growth rate in percentage: $r = 0.01349 \times 100 \approx 1.35\%$.

Result: The annual population growth rate of Nepal during 2001–2011 by the exponential method is about 1.35% per year.

Given: Elderly population in 2001, $P_0 = 18{,}250$; in 2011, $P_t = 23{,}140$; time $t = 2011 - 2001 = 10$ years.

Formula (exponential growth method):

$P_t = P_0 e^{rt} \quad\Rightarrow\quad r = \frac{\ln(P_t / P_0)}{t}$

Calculation:

$\frac{P_t}{P_0} = \frac{23{,}140}{18{,}250} = 1.2679$

$\ln(1.2679) = 0.2374$

$r = \frac{0.2374}{10} = 0.02374$

In percentage, $r = 0.02374 \times 100 \approx 2.37\%$.

Result: The annual exponential growth rate of the elderly population of the city during 2001-2011 is about 2.37% per year.