Aufgabe:
a) In 1627, the British bought the island Manhattan from Native Americans for 24 Dollars. Assuming the value was increasing exponentially, by how many percent was it growing every year?
b) If emperor Augustus had invested 1 Rappen in the year 0 and assuming 4% annual interest: How much would Augustus' descendants own today?
How many gold spheres of the size of the earth would have the same value? (Density of gold 19.29*10^3kg/m3, earth's radius 6371km, gold price in 2013: 35'000Fr./kg)
Problem/Ansatz:
a) 6000000000 = 24*(1+X/100)^343
b) ((4/3*pi*(6371000)^3)*19.29*10^3*35000) / 0.01*(1.04)^2015
Lösungen a)5.8%
b) 287 earth-size spheres
Meine Gleichungen scheinen nicht Richtig zu sein, jedoch finde ich keine Fehler..