net mineralization rate equation

Can someone help me understand this equation for net mineralization rate?

dN/dt = -kN

I understand dN as the change in organic N per unit soil volume, and k as the decay coefficient, and dt as change in time. if k has the units of 1/t then both sides of the equation are the same thing, what is the point of this equation? and how is it used? can someone relate this to C:N ratio and explain how i can use this formula in a calculation?

thank you!

CS, can you give me a bit more detail where you see this formula (e.g. in Brady or ?) as we do not cover decay constants in APBI200. 1) net mineralization: understand that both mineralization and immobilization processes are occurring simultaneously. Net mineralization implies that mineralization > immobilization, and thus N is being converted to inorganic / available forms at a rate greater than that required by organisms, thus N is available for plants.

2) C:N ratio is an indicator of the rate of SOM mineralization. A C:N = 25 is ideal for micro-organisms (to meet their metabolic C and N requirements, including respiration) thus C:N < 25 will result in net mineralization, and a wide C:N ratio >> 25 will result in net immobilization.

3) decay constants are used to express the exponential relationship between SOM decomposition and time. The rate of decomposition is influenced by environmental factors (tempertature, moisture, pH etc.) and the composition (type) of organic matter. Thus soil organic matter with a wide C:N ratio (e.g. 200:1) decomposes more slowly, and thus impacts the k-value (i.e. the decomposition rate)

If you are interested in learning more about k-values the article "Organic Matter Decomposition in Western United States Forests" by Edmonds gives a pretty good overview. BUT k-values are not something covered in APBI200