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 year, then the number of transistors is multiplied by 100.15. More generally, the rule is that if time increases by t years, then the number of transistors is multiplied by 100.15t. For example, after 8 years the number of transistors is multiplied by 100.15×8, or about 16. The Itanium 9300 Series processor was introduced by Intel Corporation in the year 2010. (a) If a chip were introduced in the year 2017, how many times the transistors of the Itanium 9300 Series would you expect it to have? Round your answer to the nearest whole number. times the transistors (b) The limit of conventional computing will be reached when the size of a transistor is on the scale of an atom. At that point the speed of a chip will be 1000 times the speed of the Itanium 9300 Series. When, according to Moore's law, will that limit be reached? (c) Even for unconventional computing, the laws of physics impose a limit on the speed of computation.† The fastest speed possible corresponds to having about 1040 times the number of transistors as on the Itanium 9300 Series. Assume that Moore's law will continue to be valid even for unconventional computing, and determine in what year this limit will be reached. Round your answer to the nearest century.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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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 year, then the number of transistors is multiplied by

10^0.15.

More generally, the rule is that if time increases by t years, then the number of transistors is multiplied by

10^0.15t.

For example, after 8 years the number of transistors is multiplied by

10^0.15×8,

or about 16. The Itanium 9300 Series processor was introduced by Intel Corporation in the year 2010.

(a) If a chip were introduced in the year 2017, how many times the transistors of the Itanium 9300 Series would you expect it to have? Round your answer to the nearest whole number.
times the transistors

(b) The limit of conventional computing will be reached when the size of a transistor is on the scale of an atom. At that point the speed of a chip will be 1000 times the speed of the Itanium 9300 Series. When, according to Moore's law, will that limit be reached?

(c) Even for unconventional computing, the laws of physics impose a limit on the speed of computation.† The fastest speed possible corresponds to having about

10⁴⁰

times the number of transistors as on the Itanium 9300 Series. Assume that Moore's law will continue to be valid even for unconventional computing, and determine in what year this limit will be reached. Round your answer to the nearest century.

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