a ( t ) = 3000 * 1.6 ^t
b ( t ) = 8000 * 1.2 ^t
Verdoppelung von a
6000 = 3000 * 1.6 ^t
2 = 1.6 ^t | ln ( )
ln ( 2 ) = ln ( 1.6 ^t )
ln ( 2 ) = t * ln ( 1.6 )
t = ln ( 2 ) / ln ( 1.6 ) =
t = 1.475 Tage
a ( t ) = 3000 * 1.6 ^t = 50 * 100^2
1.6 ^t = 33.3333 | ln ( )
t * ln ( 1.6 ) = ln ( 33.3333 )
t = 7.46 Tage
a ( t ) = b ( t )
3000 * 1.6 ^t = 8000 * 1.2 ^t
1.6 ^t / 1.2 ^t = 8000 / 3000
( 1.6 / 1.2 ) ^t = 8 / 3
t * ln ( 1.6 / 12 ) = ln ( 8 / 3 )
t = 0.9808 / 0.2877
t = 3.41 Tagen
a ( t ) + b ( t ) = 900 * 100^2
3000 * 1.6 ^t + 8000 * 1.2 ^t = 900 * 10^4
3 * 1.6 ^t + 8 * 1.2 ^t = 9000
Nänherungsweise
t = 10
3 * 1.6^10 + 8 * 1.2 ^10 = 330 + 49.53
t = 20
3 * 1.6^20 + 8 * 1.2 ^20 = 36268 + 307
t = 17
3 * 1.6^17 + 8 * 1.2 ^17 = 8854 + 177 = 9031
Ungefähr nach 17 Tagen