Natural systems (respiring animals, decomposition, fires, the ocean) contribute approximately 700 giga-tons of Carbon (GtC) to the atmosphere each year. About how much Carbon do human activities contribute to the atmosphere each year?

Around 25-30 gigatons.

Explanation:

Although natural processes do produce much more carbon dioxide than humans, its a delicate balance and all of that carbon dioxide is absorbed back. However, when humans arrived, they disrupted that balance, and even with the relatively small amount it is creating big problems.