ln(D(t))=ln(50)+tln(0.9)

Lösung

ln (D (t)) = ln (50) + t ln (0.9)

t = - \frac{W ( - \frac{50 l n ( 0.9 )}{D} )}{ln ( 0.9 )}

Schritte zur Lösung

ln (D (t)) = ln (50) + t ln (0.9)

Wenn

f (x) = g (x),

dann

a^{f (x)} = a^{g (x)}

e^{l n (D t)} = e^{l n (50) + t l n (0.9)}

Vereinfache

e^{l n (D t)} : D t

Vereinfache

e^{l n (50) + t l n (0.9)} : 50 \cdot 0. 9^{t}

D t = 50 \cdot 0. 9^{t}

Löse

D t = 50 \cdot 0. 9^{t} : t = - \frac{W ( - \frac{50 l n ( 0.9 )}{D} )}{ln ( 0.9 )}

t = - \frac{W ( - \frac{50 l n ( 0.9 )}{D} )}{ln ( 0.9 )}

Überprüfe die Lösungen:

t = - \frac{W ( - \frac{50 l n ( 0.9 )}{D} )}{ln ( 0.9 )}

Wahr

Deshalb ist die Lösung

t = - \frac{W ( - \frac{50 l n ( 0.9 )}{D} )}{ln ( 0.9 )}

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