2ways in which the carbon is stored for a long time

1) Carbon can be stored as chemical energy in the cells of the plant or the animal. So, the carbon will stay stored as part of the organic material that makes up the plant or animal until it dies. When a plant or animal dies, it either decomposes and the carbon is released back into the environment; or the organic material of the organism is buried and transformed over millions of years into coal, oil, or natural gas. 
2)Another way that carbon is stored for long periods of time is when carbon is used by ocean organisms. Many ocean creatures use calcium carbonate (CaCO3) to make their shells or to make the reef material where coral animals live. When algae die, their organic material becomes part of the ocean sediments, which may stay at the bottom of the ocean for many years. Over millions of years, those same ocean sediments can be forced down into the mantle when oceanic crust is consumed in deep ocean trenches. As the ocean sediments melt and form magma, carbon dioxide is eventually released when volcanoes erupt.