Question #e1391dd6 - SAT Suite Question Bank

Modded SAT Question Bank by Abdullah Mallik

According to Moore’s law, the number of transistors included on microprocessors doubles every 2 years. In 1985, a microprocessor was introduced that had 275,000 transistors. Based on this information, in which of the following years does Moore’s law estimate the number of transistors to reach 1.1 million?

1987
1989
1991
1994

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Correct Answer:

Rationale

Choice B is correct. Let x be the number of years after 1985. It follows that $x over 2$ represents the number of 2-year periods that will occur within an x-year period. According to Moore’s law, every 2 years, the number of transistors included on microprocessors is estimated to double. Therefore, x years after 1985, the number of transistors will double $x over 2$ times. Since the number of transistors included on a microprocessor was 275,000, or .275 million, in 1985, the estimated number of transistors, in millions, included x years after 1985 can be modeled as $0 point 2 7 5 times 2 raised to the x over 2 power$ . The year in which the number of transistors is estimated to be 1.1 million is represented by the value of x when $1 point 1 equals, 0 point 2 7 5, times 2 raised to the x over 2 power$ . Dividing both sides of this equation by .275 yields $4 equals, 2 raised to the x over 2 power$ , which can be rewritten as $2 squared equals, 2 raised to the x over 2 power$ . Since the exponential equation has equal bases on each side, it follows that the exponents must also be equal: $2 equals x over 2$ . Multiplying both sides of the equation $2 equals x over 2$ by 2 yields $x equals 4$ . Therefore, according to Moore’s law, 4 years after 1985, or in 1989, the number of transistors included on microprocessors is estimated to reach 1.1 million.

Alternate approach: According to Moore’s law, 2 years after 1985 (in 1987), the number of transistors included on a microprocessor is estimated to be $2 times 275,000$ , or 550,000, and 2 years after 1987 (in 1989), the number of transistors included on microprocessors is estimated to be $2 times 550,000$ , or 1,100,000. Therefore, the year that Moore’s law estimates the number of transistors on microprocessors to reach 1.1 million is 1989.

Choices A, C, and D are incorrect. According to Moore’s law, the number of transistors included on microprocessors is estimated to reach 550,000 in 1987, 2.2 million in 1991, and about 6.2 million in 1994.

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