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Fordoblingskonstant

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En eksponentielt voksende funktion f(x)=b\cdot a^x. Hvis a>1 fordobles y den i løbet af et bestemt tidsrum, uanset udgangspunktet. Det bestemte tidsrum = fordoblingskonstanten = T_2

EksempelEdit

For at demonstrere situationen er det godt at have et koordinatsystem. Vi antager at fordoblingskonstanten er 2.

Hver eneste gang T_2 lægges til x-værdien fordobles y-værdien. fx: (1,2) (3,2) (5,4) (7,8) (9,16) (11,32) osv.

FormelEdit

T_2 = \frac{log(2)}{log(a)}

T_{\frac{1}{2}} = \frac{log(\frac{1}{2})}{log(a)}

Eksempel:

2^x=op5

log(2^x)=log(5)

x\cdot log(2)=log(5)^3

x=\frac{log(3)}{sin(2)}=63,238

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