Matematik
Eksponentielle funktioner / regression?
Hej
jeg har et problem med denne opgave:
<table class="MsoTableMediumGrid2Accent5" border="1" cellspacing="0" cellpadding="0" style="border-collapse:collapse;border:none;mso-border-alt:solid #4BACC6 1.0pt; mso-border-themecolor:accent5;mso-yfti-tbllook:1184;mso-padding-alt:0cm 5.4pt 0cm 5.4pt"> <td width="109" valign="top" style="width:81.45pt;border:none;background:white; mso-background-themecolor:background1;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal;mso-yfti-cnfc:517"><span style="font-family:"Cambria","serif"; mso-ascii-theme-font:major-latin;mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:major-fareast;mso-hansi-theme-font:major-latin; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; color:black;mso-themecolor:text1">År</o:p> <td width="109" valign="top" style="width:81.45pt;border:solid #4BACC6 1.0pt; mso-border-themecolor:accent5;background:#EDF6F9;mso-background-themecolor: accent5;mso-background-themetint:25;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal;mso-yfti-cnfc:1"><span style="font-family:"Cambria","serif"; mso-ascii-theme-font:major-latin;mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:major-fareast;mso-hansi-theme-font:major-latin; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; color:black;mso-themecolor:text1">2000</o:p> <td width="109" valign="top" style="width:81.5pt;border:solid #4BACC6 1.0pt; mso-border-themecolor:accent5;border-left:none;mso-border-left-alt:solid #4BACC6 1.0pt; mso-border-left-themecolor:accent5;background:#EDF6F9;mso-background-themecolor: accent5;mso-background-themetint:25;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal;mso-yfti-cnfc:1"><span style="font-family:"Cambria","serif"; mso-ascii-theme-font:major-latin;mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:major-fareast;mso-hansi-theme-font:major-latin; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; color:black;mso-themecolor:text1">2004</o:p> <td width="109" valign="top" style="width:81.5pt;border:solid #4BACC6 1.0pt; mso-border-themecolor:accent5;border-left:none;mso-border-left-alt:solid #4BACC6 1.0pt; mso-border-left-themecolor:accent5;background:#EDF6F9;mso-background-themecolor: accent5;mso-background-themetint:25;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal;mso-yfti-cnfc:1"><span style="font-family:"Cambria","serif"; mso-ascii-theme-font:major-latin;mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:major-fareast;mso-hansi-theme-font:major-latin; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; color:black;mso-themecolor:text1">2006</o:p> <td width="109" valign="top" style="width:81.5pt;border:solid #4BACC6 1.0pt; mso-border-themecolor:accent5;border-left:none;mso-border-left-alt:solid #4BACC6 1.0pt; mso-border-left-themecolor:accent5;background:#EDF6F9;mso-background-themecolor: accent5;mso-background-themetint:25;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal;mso-yfti-cnfc:1"><span style="font-family:"Cambria","serif"; 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mso-border-top-themecolor:accent5;background:white;mso-background-themecolor: background1;padding:0cm 5.4pt 0cm 5.4pt"> <p class="MsoNormal" style="margin-bottom:0cm;margin-bottom:.0001pt;line-height: normal;mso-yfti-cnfc:68"><span style="font-family:"Cambria","serif"; mso-ascii-theme-font:major-latin;mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:major-fareast;mso-hansi-theme-font:major-latin; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; color:black;mso-themecolor:text1">Pris</o:p> <td width="109" valign="top" style="width:81.45pt;border:solid #4BACC6 1.0pt; mso-border-themecolor:accent5;border-top:none;mso-border-top-alt:solid #4BACC6 1.0pt; mso-border-top-themecolor:accent5;mso-border-top-alt:1.0pt;mso-border-left-alt: .75pt;mso-border-bottom-alt:1.0pt;mso-border-right-alt:.75pt;mso-border-color-alt: #4BACC6;mso-border-themecolor:accent5;mso-border-style-alt:solid;background: #A5D5E2;mso-background-themecolor:accent5;mso-background-themetint:127; 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mso-bidi-theme-font:major-bidi;color:black;mso-themecolor:text1">2490</o:p>a) Vis at nyprisen for en computer, med god tilnærmelse er en eksponentiel aftagende funktion f, hvor x er antal år efter 2000.
b) Bestem en forskrift for f.
c) Bestem halveringskonstanten.
d) Giv et skøn over nyprisen 1. januar 2015, hvis den eksponentielle udvikling fortsætter.
e) Bestem det årlige procentvise fald i nyprisen svarende til denne udvikling.
Jeg aner simpelthen ikke hvordan jeg skal opstille en formel for opgaverne, skal jeg bruge eksponentiel regression, eller opstille en anden formel? Jeg håber der er nogen der kan hjælpe på vej med opgaverne :)
Mvh
Svar #2
01. april 2011 af Em02 (Slettet)
Har du en formel eller noget jeg kan bruge til det? Sidder med det problem, at min lærer har givet en emneopgave for, om noget som vi ikke har lært endnu..
Svar #5
01. april 2011 af Tyrael (Slettet)
#0:
a): Tegn punkterne ind i fx Excel i et enkeltlogartimisk koordinatsystem. Hvis tendenslinjen er lineær, og punkterne omtrent danner en lineær sammenhæng mellem x og y (i et enkeltlogartimisk koordinatsystem vel og mærke!), er der altså tale om en eksponentiel funktion. Om den er voksende eller aftagende, kan du nok selv se.
b): Eksponentiel regression kan foretages vha. forskellige CAS-værktøjer, fx TI-89, Graph, Excel - ja, der er talrige muligheder!
Når du anvender regression, skal du huske at angive regressionstypen samt konstaterne der forekom ved regressionen - dernæst skriver du hele forskriften.
I (#3 og) #4 har Mathon allerede gjort dette for dig.
c) Bes tem halveringskonstanten
Halveringskonstanten er givet ved T1/2 = ln(1/2)/(ln(a))
Der indsættes
T1/2 = ln(1/2)/(ln(a)) = ln(1/2)/(ln(0,89945)) = 6,54
Ca. hvert 6 år halveres prisen altså.
d): Det kan du selv give et skøn på - ellers må du forsøge, og så skal vi nok hjælpe.
Svar #6
03. april 2011 af Em02 (Slettet)
Tusinde tak for svarene, jeg har fået løst alle opgaver nu, undtagen e), som jeg stadig har problemer med, men nu vil jeg lige prøve igen igen og se om jeg kan finde svaret :)
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