Figure 1. Moore's Law: Note that in 1982, ICs had about 100,000 transistors, whereas in 2016, they had about 10^10.
Moore’s Law posits that the number of transistors doubles every two years. If so, "b" should be 0.5. It ends up that "b", from the solution in Figure 2, is 0.4885, so a double occurs about 1/0.4885 =2.047 years, but this number is really close to two years. The solution follows:
Figure 2. The Solution of a and b in the Moore's law equation.
BTW, congrats to Indium Corporation's Dr. Huaguang Wang as he got a close solution.