Moore's law states that the transistor density on integrated circuits doubles every 2 years. So this is an exponential function. My question is simple; what function of the form $y= a \times e^{bx+c}$ would best describe this growth (with a length of 1 on the x-axis corresponding to 1 month of time)? If there are other functions which are not of the aforementioned form, that would be good too. Please also show the derivation.
[Math] Which function would best describe Moore’s law
functions
Best Answer
The $c$ doesn't matter-you can do $e^{bx+c}=e^{bx}e^c$ and absorb it into $a$. But $a$ doesn't matter either-that just sets the scale, or the zero of time. We are just looking for $b$. After $24$ months things have doubled, so we need $2=e^{24b}$ Taking logs we get $b=\frac {\log 2}{24}$