Chapter 4.5, Problem 7E

Reminder Round all answers to two decimal places unless otherwise indicated.

Moore’s Law The speed of a computer chip is closely related to the number of transistors on the chip, and the number of transistors on a chip has increased with time in a remarkably consistent way. In fact, in the year $1965$, Dr. Gordon E. Moore (now chairman emeritus of Intel Corporation) observed a trend and predicted that it would continue for a time. His observation, now known as Moore’s law, is that every two years or so a chip is introduced with double the number of transistors of its fastest predecessor. This law can be restated in the following way: If time increases by $1\text{year}$, then the number of transistors is multiplied by ${10}^{0.15}$.More generally, the rule is that if time increases by $t\text{years}$, then the number of transistors is multiplied by ${10}^{0.15t}$.For example, after $8\text{years}$, the number of transistors is multiplied by ${10}^{0.15\times 8}$, or about $16$. The $6\text{th}$ generation Core processor was released by Intel Corporation in the year $2015$.

a. If a chip were introduced in the year $2022$, how many times the transistors of the 6^th generation Core would you expect it to have? Round your answer to the nearest whole number.

b. The limit of conventional computing will be reached when the size of a transistors on a chip will be $200$ times that of the 6^th generation Core. When, according to Moore’s law, will that limit be reached?

c. Even for unconventional computing, the law of physics impose a limit on the speed of computation. The fastest speed possible corresponds to having about ${10}^{40}$ times the number of transistors as on the 6^th generation Core. Assume that Moore’s law will continue to be valid even for unconventional computing, and determine when this limit will be reached. Round your answer to the nearest century.