4000=6000/1+29e^-0.4t

I assume this is  \(4000=\frac{6000}{1+29*e^{-0.4t}}\)

 

Divide both sides by 2000 and multiply both sides by the denominator of the right-hand side to get

 

\(1+29e^{-0.4t}=\frac{3}{2}\)

 

Subtract 1 from each side and divide both sides by 29 to get

 

\(e^{-0.4t}=\frac{1}{58}\)

 

Take log to base e (ln) of both sides and divide by -0.4 to get

 

\(t=-\frac{1}{0.4\times \ln{58}}\)

 

or t ≈ 10.151