Which function would best describe Moore's law
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.
$\endgroup$2 Answers
$\begingroup$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 $b=\frac {\log 2}{24}$
$\endgroup$ 2 $\begingroup$
Log2/24 on your example gives growth which is excellent and in addition it would probably want to include some coefficient of friction to account for an eventual equilibrium point. It's like to see more thoughts on this and or be looking forward some more formulation on Moore's law so as to compare to, for example, Wright's (ARK) Law.
$\endgroup$
