Question

Moore’s Law In 1965, Gordon Moore observed that the number of transistors that could be placed on an integrated circuit was approximately doubling each year, and he predicted that this trend would continue for another decade. In 1975, Moore revised the doubling time to every two years, and this prediction became known as Moore’s Law.

a. In 1979, Intel introduced the Intel 8088 processor; each of its integrated circuits contained 29,000 transistors. Use Moore’s revised doubling time to find a function y(t) that approximates the number of transistors on an integrated circuit t years after 1979.

Accepted Answer

Identify the initial value and the growth pattern: In 1979 (which corresponds to t = 0), the number of transistors is 29,000. This is our initial value, so $$y(0) = 29000. $$Understand the doubling time: According to Moore's revised law, the number of transistors doubles every 2 years. This means the quantity grows exponentially with a doubling period of 2 years. Write the general form of the exponential growth function: Since the quantity doubles every 2 years, the function can be expressed as $$y(t) = y_0$ 	imes 2$$^{\frac{t}$${2}}$$, where $$y_0 is $$the initial number of transistors and $$t is $$the number of years after 1979. Substitute the initial value into the function: Replace $$y_0$$ with 29,000 to get $$y(t) = 29000 	imes 2$$^{\frac{t}$${2}}. $$Interpret the function: This function $$y(t)$$ gives the approximate number of transistors on an integrated circuit $$t$$ years after 1979, assuming the doubling every two years continues.

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Key Concepts

Exponential Growth

Doubling Time

Function Modeling with Initial Conditions