Aloha :)
Faustregel zur schnellen Abschätzung der Verdopplung: \(\frac{72}{4,5}=16\)
Genaue Rechnung:
$$\left.K\cdot\left(1+\frac{4,5}{100}\right)^n=2\cdot K\quad\right|\quad:\,K$$$$\left.\left(1+\frac{4,5}{100}\right)^n=2\quad\right|\quad\text{Klammer ausrechnen}$$$$\left.1,045^n=2\quad\right|\quad\ln(\cdots)$$$$\left.\ln(1,045^n)=\ln(2)\quad\right|\quad\text{verwende }\ln(a^b)=b\cdot\ln(a)$$$$\left.n\cdot\ln(1,045)=\ln(2)\quad\right|\quad:\,\ln(1,045)$$$$n=\frac{\ln(2)}{\ln(1,045)}\approx15,7473$$
