Length growth of a fish The average length L (in mm) of fish larvae of the white croaker (Genyonemus Lineatus), a fish from the family of umber fish, after t days, is well described by the mathematical formula \[L=-0.833+0.242t\] The growth rate is 0.242 millimetres per day. The average length after 10, respectively. 40 days is 1:59, respectively. 8.85 mm.

Source: Millar et al (2011), "Queen Fish (queenfish) and White Croacker (white croaker) Larval Growth Parametres" SCIAENID Larval AGE AND GROWTH, CalCOFI Vol.. 52, 75-79.

Zero-order reaction kinetics The gas dinitrogen monoxide \(\mathrm{N}_2\mathrm{O}\) (also known as nitrous oxide) dissolves into nitrogen gas \(\mathrm{N}_2\) and oxygen gas \(\mathrm{O}_2\) in the presence of finely divided gold powder, which acts as a catalyst: \[2\mathrm{N}_2\mathrm{O}\stackrel{\mathrm{Au}}{\longrightarrow}2\mathrm{N}_2+\mathrm{O}_2\]

It is striking, that the reaction rate does not depend on the amount of starting materials or reaction products, but it is constant. The reason for this, is that the gold surface can only accommodate a limited number of molecules and the dinitrogen monoxide concentration has no influence on it. The concentration \(C\) of dinitrogen monoxide as a function of time \(t\) can therefore be described as \[C'(t)=-k\] for certain constant \(k\). The solution of this differential equation gives a linear function \[C(t)=C_0-k\cdot t,\] where \(C_0\) is the concentration at time \(t=0\) is.