Decomposers are living organisms, so their rate of decomposition depends on the conditions around them. Three factors matter most: temperature, water content and oxygen availability.
Temperature. As temperature rises, decomposers respire and grow faster and their enzymes work faster, so decomposition speeds up. This continues up to an optimum temperature. At much higher temperatures the enzymes denature and the decomposers die, so decomposition slows or stops. In cold conditions decomposition is very slow.
Water content. Decomposers need water, so moist material decomposes faster than dry material. If material is waterlogged, air is pushed out of it and there is little oxygen.
Oxygen availability. Aerobic decomposition uses oxygen and releases carbon dioxide and water. It is fast. Anaerobic decomposition happens without oxygen. It is slower and releases the gas methane. Turning a compost heap lets air in, and a warm, moist, well aerated heap decays quickly.
We can calculate a rate of decomposition: rate = change in mass ÷ time. If a pile of leaves loses 6 g in 3 weeks, the rate is 6 ÷ 3 = 2 g per week.