Is there a formula to work out the answer to â how many doubles are needed to reach a certain amountâ? For instance, start with 50. double it = 100, double again =200 and so on. How many doubles, in this way to reach 200 million? Thanks
50 x 2<sup>n</sup> = 200,000,000 2<sup>n</sup> = 4,000,000 n = ln 4,000,000 / ln 2 &asymp 15.20 / 0.69 &asymp 21.93 --> 22 doubles Check: 50 x 2<sup>22</sup> &asymp 209.7M > 200M If a calculator isn't handy or doesn't have log function, just remember that 2<sup>10</sup> = 1,024 &asymp 1,000. So for every 10 "doubles" simply add 3 zeros to your starting number. For example: 50 to start off 10 doubles --> ~50,000 20 doubles --> ~50,000,000 and so on.