# Exponential growth with fixed coefficient

### Definition

This law changes the concentration of a class depending on an other class concentration (or eventually itself), and two fix coefficients $k$ and $\alpha_k$ as shown here:

$\frac{dC_i}{dt}=k C_j^{\alpha_k}$

### Classic use

Numerous solutes have a first-order kinetics with an equation similar to :

$\frac{dC_{Ni}}{dt}= - k_{Ni} C_{Ni}$

where $k_{Ni}$ is the reaction constant (which is the inverse of a time). For instance, bacteriological oxygen demand (DBO_5 ), has a constant around 0.3 days -1 . This degradation models the process of water auto-purification in streams.

### Specifications

• Law’s ID : 201
• Number of acting classes : 2
• Number of parameters : : 2

Acting classes :

• $C_i$ : the class modified by the law
• $C_j$ : the parameter class of the law

Parameters :

• $k$ : reaction constant
• $\alpha_k$ : reaction order