equation

to solve for t    first divide both sides by 100000

2=e^.0475t   take ln of both sides

ln 2 = .0475t

14.59=t

200000=100000e^.0475t    divide both sides by 100000

2 = e^[.0475t]     take the ln of both sides

ln 2  = ln e^[.0475t]      and by a log property we can write

ln 2  =  [ .0475t] * lne      the ln e  = 1......so we can drop this and we're left with

ln 2  = .0475t     divide both sides by .0475

ln 2 / .0475  = t   = about 14.59