That's a bit too simplistic for my taste, but I think you're on the right track. Exponential decay implies that the rate at which methane disappears is equal t

That's a bit too simplistic for my taste, but I think you're on the right track. Exponential decay implies that the rate at which methane disappears is equal to the total amount divided by the average lifetime, so with an additional 0.5 / year, you reach a steady state when (total amount / average lifetime) = (0.5 / year), hence when the total amount is 3.5. Assuming we already were in a steady state initially there should be an additional 1/7 / year from natural sources bringing the total to 4.5.