Nonlinear functions SAT question

Choice B is correct. Let x be the number of years after 1985. It follows that 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 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 . The year in which the number of transistors is estimated to be 1.1 million is represented by the value of x when . Dividing both sides of this equation by .275 yields , which can be rewritten as . Since the exponential equation has equal bases on each side, it follows that the exponents must also be equal: . Multiplying both sides of the equation by 2 yields . 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 , or 550,000, and 2 years after 1987 (in 1989), the number of transistors included on microprocessors is estimated to be , 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.