what does t equal

2e^(3t) = 400

e^(3t) = 200

3t = ln 200

t = (ln 200)/3

I think this might be :

2e ^(3t) = 400 divide both sides by 2

e^(3t) = 200 take the Ln of both sides

Ln e^(3t) = Ln 200 and we can write

(3t) Ln e = Ln 200 Ln e = 1 so we can ignore this

3t = Ln 200 divide both sides by 3

t = Ln 200 / 3 ≈ 1.766