Moore’s Law In 1965, Gordon Moore observed that the number of ...

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

Welcome back, everyone. A certain microprocessor had 60,000 transistors and 1992. If the number of transistors doubles every 4 years, what is the function Y of T for the number of transistors 2 years after 1992? For this problem, because it says doubles every 4 years, we have to understand that this model is an exponential growth. So let's write a general form of an exponential growth function. YFT is going to be equal to Y subscript 0, the initial amount multiplied by E raises the power of KT, right, where T is time and K is the growth rate. So what we want to do is simply understand that our reference point is 1992, which is represented by T equals 0. And if T equals 0, well, we can say that. Y 0 equals Y 0, right? That's our initial amount. In this case, Y models transistors, so the initial number of transistors Y subscript 0 is 60,000. This is what we have in the problem. So we have identified why subscript 0, and the final part that we want to identify is the. Great constant K. It says doubles every 4 years. Let's recall that doubling time. Capital T subscript 2 is represented by a formula LN of 2 divided by K. So now rearranging this formula, we can show that K is equal to LN of 2, divided by the doubling time. Which is equal to LN of 2 divided by 4, right? Because our doubling time is 40 years. Well then, so now we have our K, we have Y subscript 0, and we can say that this model is Y of T equals 60,000. Multiplied by E to the power of. LN of 2 divided by 4 multiplied by T. That's our final answer and thank you for watching.

Watch next