0=0.012t^2*e^(-0.11t)-0.25t^2*e^(-0.5t)

Hallo Dutti!

0 = 0.012t^2 * e^(- 0.11t) - 0.25t^2 * e^(-0.5t)

^{0.012t2 * e- 0.11t} =  0.25t² * e^-0.5t

0.012t² / 0.25t² = e^-0.5t / e^-0.11t

0.048 = e^{(- 0.5t + 0.11t)}

ln 0.048 = ln e ^{(- 0.5t + 0.11t)}

ln 0.048 = - 0.5t + 0.11t

ln 0.048 = - 0.39 t

t = ln 0.048 / - 0.39

t = - 3.0365542607 / - 0.39

t = 7.7863658479

Probe:

0.012 * 7.786² * e^{-0.11 * 7.786} = 0.25 * 7.786² * e^{-0.5 * 7.786} 

0.3089 = 0.3089

q.e.d.

Gruß asinus :- )

 !