$$ \frac {dy} {dt}=ky(a-y)\text { or } \frac {dy} {dt} =ky(1-\frac y a)\Rightarrow y=\frac a {1+Ce^{-akt}} $$

• when y is smaller than a then $\frac {dy}{dt}\approx ky$
• $\frac a 2$\ is the point of inflection
• the limit is a
• $y→a,\frac {dy} {dt}→0$