|
|
| Rad 1: |
Rad 1: |
| | == Test av javascript inäddat == |
|
| |
|
| <html>
| | {{:test av javascript inbäddat}} |
| | |
| <script type="text/javascript" language="javascript" src="
| |
| http://www.geogebra.org/web/4.2/web/web.nocache.js"></script><article class="geogebraweb" data-param-width="530" data-param-height="467"
| |
| data-param-showResetIcon="true" data-param-enableLabelDrags="true" data-param-showMenuBar="false" data-param-showToolBar="false" data-param-showAlgebraInput="true" enableLabelDrags="true" data-param-ggbbase64="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"></article>
| |
| | |
| </script>
| |
| </body>
| |
| </html>
| |
| == Exponentialfunktioner ==
| |
| | |
| === Jämför ===
| |
| | |
| Jämför med den allmänna formen för andragradsfunktionen:
| |
| | |
| : <math>y = ax^2 + bx + c </math> (bortse från de sista termerna)
| |
|
| |
| : <math>y = ax^2 </math> (a är en konstant, vi kan lika gärna skriva c)
| |
|
| |
| : <math>y = C \cdot x^2 </math> (tänk nu att vi kastar om x och 2, C är en konstant )
| |
|
| |
| : <math>y = C \cdot 2^x </math> (här har vi ett exempel på en exponentialfunktion)
| |
|
| |
| : <math>y = C\cdot 1.5^x = C \cdot (\frac{3}{2})^x</math> (Vi kan ha olika tal som höjs upp i x)
| |
|
| |
| : <math>y = C \cdot 0.5^x = C \cdot (\frac{1}{2})^x = C \cdot (2^{-1})^{x}= C \cdot 2^{-x} </math> | |
| | |
| på generell form:
| |
| | |
| : <math>y = C \cdot a^x </math>
| |
| | |
| : talet '''a kallas basen'''. '''x är exponenten'''
| |
| | |
| === Växande ===
| |
| | |
| Tänk på pengar på banken med ränta varje år. Pengarna växer med ränta på ränta. 15 % innebär en tillväxtfaktor om 1.15 (förändringsfaktorn). Antag att man har 2000 kr från början. Tillväxten blir då exponentiell. Det tar bara fem år till en fördubbling.
| |
| | |
| <html>
| |
| | |
| <script type="text/javascript" language="javascript" src="
| |
| http://www.geogebra.org/web/4.2/web/web.nocache.js"></script><article class="geogebraweb" data-param-width="626" data-param-height="417"
| |
| data-param-showResetIcon="true" data-param-enableLabelDrags="true" data-param-showMenuBar="true" data-param-showToolBar="true" data-param-showAlgebraInput="false" enableLabelDrags="true" data-param-ggbbase64="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"></article>
| |
| | |
| </script>
| |
| </body>
| |
| </html>
| |
| Filen ligger på HD.
| |