In 1965, Intel cofounder Gordon Moore predicted that the number of transistors on a computer chip would double approximately every 2 years. This prediction is known as Moore's Law. Data for four Intel processors are shown in the table. (Note: Use the concepts of half-life or doubling time.)
Intel Processors and Transistors
Year Processor Transistors
(million)
1971 4004 0.0023
1993 Pentium 3.1
2003 Itanium 2 220
2010 Tukwila 2,000
(a) Using a doubling time of 2 years and the 4004 processor as the starting information, write the function of the model that gives the number of transitors in millions t years after 1971, with data from 0 ≤ t ≤ 39.
(Round all numerical values to four decimal places.) m(t) =
(b) Align the data in the table so that t = 0
in 1971. Find the function for the exponential model that gives the number of transitors in millions with data from 0 ≤ t ≤ 39.
(Round all numerical values to three decimal places.)
T(t) =
(c) Does the model from the data confirm Moore's prediction?
Yes. The model from the data is very close to Moore's prediction. No. The model from the data is significantly different from Moore's prediction.