Lub Npe: Cov Lus Nug Piv Txwv thiab Kev Sib Tham Txog Cov Ntaub Ntawv Txog Cov Neeg
Pendahuluuan
Cov ntaub ntawv txog pej xeem yog cov ntaub ntawv tseem ceeb uas qhia txog cov xwm txheej ntawm ib cheeb tsam. Cov ntaub ntawv no ua lub luag haujlwm tseem ceeb hauv kev npaj kev txhim kho, kev muab kev pabcuam rau pej xeem, thiab kev txiav txim siab txog txoj cai pej xeem. Tsab xov xwm no yuav tshawb nrhiav ntau qhov teeb meem piv txwv ntsig txog cov ntaub ntawv txog pej xeem, ua raws li kev sib tham tob tob kom nkag siab zoo dua txog kev tshuaj xyuas thiab kev siv cov ntaub ntawv no.
Piv txwv lus nug 1: Xam kev loj hlob ntawm cov pej xeem
Lo lus nug:
Hauv ib lub nroog, cov pej xeem tau sau tseg ntawm 150.000 hauv xyoo 2020. Txog xyoo 2025, cov pej xeem yuav nce mus txog 165.000. Xam tus nqi nruab nrab ntawm cov pej xeem txhua xyoo siv txoj kev loj hlob exponential.
Kev Sib Tham:
Yuav kom xam tau qhov nruab nrab ntawm cov pej xeem loj hlob txhua xyoo, peb siv tau cov mis exponential population growth formula raws li nram no:
\[ P(t) = P_0 \times e^{(rt)} \]
Qhov twg:
- \( P(t) \) yog cov pej xeem kawg (2025)
- \( P_0 \) yog cov pej xeem thawj zaug (xyoo 2020)
- \( r \) yog tus nqi ntawm cov pej xeem loj hlob txhua xyoo
- \( t \) yog lub sijhawm sib nrug hauv xyoo
Nws paub tias:
\[ P_0 = 150.000 \]
\[ P(t) = 165.000 \]
\[ t = 5 \]
Peb hloov cov nqi no rau hauv qhov sib npaug:
\[ 165.000 = 150.000 \times e^{(5r)} \]
Yuav nrhiav tau tus nqi ntawm \( r \), peb daws qhov equation:
\[ \frac{165.000}{150.000} = e^{(5r)} \]
\[ 1.1 = e^{(5r)} \]
Peb siv cov logarithm ntuj ntawm ob sab ntawm qhov sib npaug:
\[ \ln(1.1) = 5r \]
\[ r = \frac{\ln(1.1)}{5} \]
\[ r \approx \frac{0.0953}{5} \]
\[ r \kwv yees li 0.01906 \]
Yog li, qhov nruab nrab ntawm cov pej xeem txhua xyoo yog nyob ib puag ncig 1,906%.
Piv txwv lus nug 2: Xam qhov sib piv ntawm kev vam khom
Lo lus nug:
Xyoo 2021, ib lub zos muaj cov ntaub ntawv pej xeem nrog cov hnub nyoog raws li nram no:
– Cov pej xeem hnub nyoog 0-14 xyoo: 8.000 tus neeg
– Cov pej xeem hnub nyoog 15-64 xyoo: 32.000 tus neeg
- Cov pej xeem hnub nyoog 65 xyoo thiab laus dua: 5.000 tus neeg
Xam tus piv ntawm kev vam khom ntawm lub zos.
Kev Sib Tham:
Qhov piv ntawm kev vam khom yog qhov piv ntawm cov pej xeem tsis muaj peev xwm ua haujlwm tau zoo (hnub nyoog qis dua 15 xyoos thiab tshaj 64 xyoos) rau cov pej xeem muaj peev xwm ua haujlwm tau zoo (hnub nyoog 15-64 xyoos). Qhov piv no muab kev pom dav dav ntawm lub nra hnyav ntawm kev lag luam rau cov pej xeem muaj peev xwm ua haujlwm tau zoo hauv kev txhawb nqa cov pej xeem tsis muaj peev xwm ua haujlwm tau zoo.
Tus qauv piv txwv ntawm kev vam khom yog:
\[ \text{Qhov Sib Piv Ntawm Kev Sib Txuas Lus} = \left( \frac{\text{Cov Neeg Muaj Hnub Nyoog 0-14 Xyoos + Muaj Hnub Nyoog 65 Xyoos thiab Siab Dua}}{\text{Cov Neeg Muaj Hnub Nyoog 15-64 Xyoos}} \right) \xeem 100\% \]
Hloov cov nqi rau hauv cov mis:
\[ \text{Sib Piv Sib Txuas} = \left( \frac{8000 + 5000}{32000} \right) \times 100\% \]
\[ \text{Sib Piv Sib Txuas} = \left( \frac{13000}{32000} \right) \times 100\% \]
\[ \text{Qhov Sib Piv Ntawm Kev Sib Txuas Lus} \kwv yees li 40.625\% \]
Yog li, qhov piv ntawm kev vam khom hauv lub zos yog li ntawm 40,625%, uas txhais tau tias txhua 100 tus neeg nyob hauv lub hnub nyoog muaj peev xwm txhawb nqa kwv yees li 41 tus neeg nyob hauv lub hnub nyoog tsis muaj peev xwm.
Piv txwv lus nug 3: Kev kwv yees cov pej xeem
Lo lus nug:
Yog tias tus nqi nce ntxiv ntawm cov pej xeem txhua xyoo hauv ib cheeb tsam yog 2% thiab cov pej xeem tam sim no yog 20.000, ces yuav muaj pes tsawg tus pej xeem hauv 10 xyoo tom ntej no?
Kev Sib Tham:
Yuav ua kom muaj kev kwv yees txog cov pej xeem, peb siv tau cov mis exponential growth formula:
\[ P(t) = P_0 \times (1 + r)^t \]
Qhov twg:
– \( P_0 = 20.000 \)
– \( r = 0.02 \) (kev loj hlob 2% ib xyoos)
– \( t = 10 \)
Hloov cov lej no rau hauv tus qauv:
\[ P(10) = 20.000 \times (1 + 0.02)^{10} \]
\[ P(10) = 20.000 \times (1.02)^{10} \]
\[ P(10) = 20.000 \times 1.21899 \]
\[ P(10) \kwv yees li 24.380 \]
Yog li, cov pej xeem kwv yees hauv 10 xyoo tom ntej no yog kwv yees li 24.380 tus neeg.
Kev kaw
Los ntawm kev nkag siab txog yuav ua li cas xam cov pej xeem loj hlob, cov piv txwv ntawm kev vam khom, thiab kev kwv yees cov pej xeem, peb tuaj yeem pom tias cov ntaub ntawv pej xeem tseem ceeb npaum li cas hauv ntau txoj cai thiab kev npaj. Cov ntaub ntawv no tsis yog tsuas yog pab tsoomfwv muab cov kev pabcuam pej xeem zoo dua xwb tab sis kuj muab kev nkag siab rau cov pej xeem txog kev txhim kho pej xeem thiab kev hloov pauv hauv lawv cov zej zog. Kev xyaum tshuaj xyuas thiab siv cov ntaub ntawv pej xeem yog ib qho kev txawj ntse muaj txiaj ntsig zoo hauv lub hnub nyoog xov xwm niaj hnub no.
