Kushandisa Mafomura Ekuwedzera
Fomura ye exponential ipfungwa yemasvomhu inowanzoitika muhupenyu hwezuva nezuva, kunyangwe isu tisingazvizivi. Patinotaura nezvekuwedzera kwevanhu, kuwedzera mubereko pamaakaundi ekuchengetedza, kupararira kwemavhairasi, kuora kwezvinhu zvine mwaranzi, uye kunyange kukura kwevashandisi vemapurogiramu edhijitari, zvese izvi zvinogona kutevedzera uchishandisa patani yakafanana: shanduko "dzinowanda" nekufamba kwenguva. Patani iyi ndiyo hunhu hukuru hwe exponentials. Chinyorwa chino chichakurukura tsananguro yefomura ye exponential, chimiro chayo chakajairika, mashandisirwo ayo, pamwe chete nemienzaniso yekushandisa uye mazano ekudzivirira zvikanganiso zvekuverenga.
1. Chii chinonzi exponential?
Muchidimbu, exponentiation inzira yekuverenga inosanganisira masimba. Kana tikanyora \(a^n\), ipapo \(a\) inonzi base uye \(n\) inonzi exponent kana simba. Muenzaniso uri nyore: \(2^3 = 8\), zvinoreva kuti 2 yakawedzerwa neyo pachayo katatu: \(2 \times 2 \times 2\).
Zvisinei, kana tichitarisa kutevedzera, "fomura yekutsanangura" inowanzoreva basa rine kukosha kunowedzera kana kuderera nechinhu chakagadziriswa mukati menguva yakatarwa. Semuenzaniso, nhamba inoramba ichikwira ne10% gore rega rega zvinoreva kuti kukosha kwayo kunowedzerwa ne1,10 gore rega rega. Iyi ipatani yekutsanangura - kwete kuwedzera nehuwandu hwakagadziriswa, asi nechikamu chakagadziriswa.
2. Chimiro chakazara chefomura ye exponential
Kune mhando mbiri dzemafomura e exponential anowanzoshandiswa:
1) Kukura/kuora kweganda (zvichienderana nenguva yakatarwa)
\[
N(t) = N_0 \kawa pa^t
\]
Information:
– \(N(t)\): kukosha panguva \(t\)
– \(N_0\): kukosha kwekutanga
– \(a\): kuwanda kwechikamu chimwe nechimwe (semuenzaniso 1,10 yekuwedzera kwe10%; 0,90 yekudzikira kwe10%)
– \(t\): nhamba yenguva (semuenzaniso makore, mwedzi, mazuva)
2) Kukura/kuora kunoramba kuripo (muenzaniso wehuwandu hunoramba huripo)
\[
N(t) = N_0 \nguva e^{rt}
\]
Information:
– \(e\) ndiyo nhamba yaEuler (inenge 2,71828)
– \(r\) mwero wekukura unoenderera mberi (unogona kuva wakanaka pakukura, asi usina kunaka pakudzikira)
– \(t\) nguva
Muzviitiko zvakawanda zvechikoro kana mashandisirwo ari nyore, chimiro chakasiyana \(N(t)=N_0 a^t\) chakakwana. Chimiro chinoenderera mberi chinowanzo shandiswa mukuongorora kwakadzama, semuenzaniso mukuverenga, fizikisi, kana kutevedzera epidemic.
3. Matanho ekushandisa fomura ye exponential
Kuti udzivise kuvhiringidzika, tevera matanho aya paunenge uchishanda pamatambudziko ekuwedzera:
1) Sarudza kukosha kwekutanga kwe \(N_0\)
Iyi ndiyo huwandu huri pakutanga kwekucherechedza (gore 1, zuva 0, zvichingodaro).
2) Kuziva kana kuri kukura kana kuora.
– Kukura: kukosha kunowedzera (factor \(a > 1\) kana \(r>0\))
– Kuora: kukosha kunowedzera kuderera (factor \(0)
