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Posted on Jul 06, 2024

im lost, can you please help me? In some applications, the variable being studied increases so quickly (exponentially) that a regular graph isn't informative. There,

im lost, can you please help me?

In some applications, the variable being studied increases so quickly ("exponentially") that a regular graph isn't informative. There, a regular graph would show data close to 0 and then a sudden spike at the very end. Instead, for these applications, we often use logarithmic scales. We replace the y-axis tick marks of 1, 2, 3, 4, etc. with y-axis tick marks of 101 = 10, 10?- = 100, 103 = 1000, 104 = 10000, etc. In other words, the logarithms of the new tick marks are equally spaced. Technology is one area where progress is extraordinarily rapid. Moore's Law states that the progress of technology (measured in different ways) doubles every 2 years. A common example counts the number of transitors per integrated circuit. A regular y-axis scale is appropriate when a trend is linear, i.e. 100 transistors, 200 transistors, 300 transistors, 400 transistors, etc. However, technology actually increased at a much quicker pace such as 100 transistors,. 1,000 transistors, 10,000 transistors, 100,000 transistors, etc. The following is a plot of the number of transistors per integrated circuit over the period 1971 - 2008 taken from https://ourworldindata.org/technological-progress (that site contains a lot of data, not just for technology). At first, this graph seems to show a steady progression until you look carefully at the yaxis it's not linear. From the graph, it seems that from 19?1 to 1981 the number of transistors went from about 1,000 to 40,000. Moore's Law predicts that in 10 years, it would double 5 times, i.e. go from 1,000 to 32,000, and the actual values (using very rough estimates) seem to support this. The following is the same plot but with the common logarithm of the y-axis shown. You can see that log(y) goes up uniformly. Part a: The number of transistors per IC in 1972 seems to be about 4,000 (a rough estimate by eye). Using this estimate and Moore's Law, what would you predict the number of transistors per IC to be 20 years later, in 1992? Prediction = Number Part b: From the chart, estimate (roughly) the number of transistors per IC in 2016. Using your estimate and Moore's Law, what would you predict the number of transistors per IC to be in 2040? Part c: Do you think that your prediction in Part b is believable? Why or why not? log(y) Moore's Law - The number of transistors on integrated circuit chips (1971-2018) Our World Moore's law describes the empirical regularity that the number of transistors on integrated circuits doubles approximately every two years. in Data This advancement is important as other aspects of technological progress - such as processing speed or the price of electronic products - are linked to Moore's law. 11 50,000,000,000 72-core Xeon Phi Centriq 2400 GC2 IPU SPARC M7 $32-core AMD Epyc IBM z13 Storage Controller Apple A12X Bionic 10 10,000,000,000 18-core Xeon Haswell-E5 Tegra Xavier SoC Xbox One main SoC Qualcomm Snapdragon 8cx/SCX8180 5,000,000,000 61-core Xeon Phi HiSilicon Kirin 980 + Apple A12 Bionic 12-core POWER HiSilicon Kirin 710 8-core Xeon Nehalem-EX 10-core Core 17 Broadwell E Six-core Xeon 7400 Qualcomm Snapdragon 835 Dual-core Itanium 20 `Dual-core + GPU Inis Core 17 Broadwell-U Quad-core + GPU GT2 Core 17 Skylake K 9 1,000,000,000 Pentium D Presler POWERS Quad-core + GPU Core 17 Haswell tanium 2 with Apple A7 (dual-core ARM64 "mobile SoC") 500,000,000 Core i7 (Quad) Itanium 2 Madison 6MO AMD K10 quad-core 2M L3 Core 2 Duo Wolfdale Pentium D Smithfield re 2 Duo Conroe Itanium 2 Mckinley Core 2 Duo Wolfdale 3M Pentium 4 Prescott-2MO Core 2 Duo Allendale `Pentium 4 Cedar Mill 8 100,000,000 AMD K8 Pentium 4 Prescott 50,000,000 Pentium 4 Northwood Barton Pentium 4 Willamette Atom Pentium II Mobile Dixon Pentium III Tualatin AMD K7 . Pentium III Coppermine ARM Cortex-A9 AMD K6-lil 7 Transistor count 10,000,000 AMD K64 Pentium III Katmai oPentium II Deschutes 5,000,000 Pentium Pro ntium II Klamath Pentium AMD K5 SA-110 Intel 80486 6 1,000,000 R4000 500,000 TI Explorer's 32-bit isp machine chip ARM700 Intel 803860 960 9 ARM 3 Motorola 68020 Dar DEC WRL 5 100,000 Motorola Intel 80286 MultiTitan 68000% ARM 50,000 Intel 80186 Intel 80869 @ Intel 8088 ARM 2 ARM 1 ARM 6 Motorola 65C816 4 10,000 TMS 1000 Zilog Z80 6809 Novix NC4016 NDO RCA 1802 5,000 12 Intel 8085 Intel 8008 BIntel 8080 MOS Technology Motorola 6502 Intel 4004 3 1,000 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 002 2004 2006 2008 2010 2012 2014 2016 18 Data source: Wikipedia (https://en.wikipedia.org/wiki/Transistor_count) The data visualization is available at OurWorldinData.org. There you find more visualizations and research on this topic. Licensed under CC-BY-SA by the author Max Roser.log(y) Moore's Law - The number of transistors on integrated circuit chips (1971-2018) Our World Moore's law describes the empirical regularity that the number of transistors on integrated circuits doubles approximately every two years. in Data This advancement is important as other aspects of technological progress - such as processing speed or the price of electronic products - are linked to Moore's law. 11 50,000,000,000 72-core Xeon Phi Centriq 2400 GC2 IPU SPARC M7 $32-core AMD Epyc IBM z13 Storage Controller Apple A12X Bionic 10 10,000,000,000 18-core Xeon Haswell-E5 Tegra Xavier SoC Xbox One main SoC Qualcomm Snapdragon 8cx/SCX8180 5,000,000,000 61-core Xeon Phi HiSilicon Kirin 980 + Apple A12 Bionic 12-core POWER HiSilicon Kirin 710 8-core Xeon Nehalem-EX 10-core Core 17 Broadwell E Six-core Xeon 7400 Qualcomm Snapdragon 835 Dual-core Itanium 20 `Dual-core + GPU Inis Core 17 Broadwell-U Quad-core + GPU GT2 Core 17 Skylake K 9 1,000,000,000 Pentium D Presler POWERS Quad-core + GPU Core 17 Haswell tanium 2 with Apple A7 (dual-core ARM64 "mobile SoC") 500,000,000 Core i7 (Quad) Itanium 2 Madison 6MO AMD K10 quad-core 2M L3 Core 2 Duo Wolfdale Pentium D Smithfield re 2 Duo Conroe Itanium 2 Mckinley Core 2 Duo Wolfdale 3M Pentium 4 Prescott-2MO Core 2 Duo Allendale `Pentium 4 Cedar Mill 8 100,000,000 AMD K8 Pentium 4 Prescott 50,000,000 Pentium 4 Northwood Barton Pentium 4 Willamette Atom Pentium II Mobile Dixon Pentium III Tualatin AMD K7 . Pentium III Coppermine ARM Cortex-A9 AMD K6-lil 7 Transistor count 10,000,000 AMD K64 Pentium III Katmai oPentium II Deschutes 5,000,000 Pentium Pro ntium II Klamath Pentium AMD K5 SA-110 Intel 80486 6 1,000,000 R4000 500,000 TI Explorer's 32-bit isp machine chip ARM700 Intel 803860 960 9 ARM 3 Motorola 68020 Dar DEC WRL 5 100,000 Motorola Intel 80286 MultiTitan 68000% ARM 50,000 Intel 80186 Intel 80869 @ Intel 8088 ARM 2 ARM 1 ARM 6 Motorola 65C816 4 10,000 TMS 1000 Zilog Z80 6809 Novix NC4016 NDO RCA 1802 5,000 12 Intel 8085 Intel 8008 BIntel 8080 MOS Technology Motorola 6502 Intel 4004 3 1,000 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 002 2004 2006 2008 2010 2012 2014 2016 18 Data source: Wikipedia (https://en.wikipedia.org/wiki/Transistor_count) The data visualization is available at OurWorldinData.org. There you find more visualizations and research on this topic. Licensed under CC-BY-SA by the author Max Roser.Moore's Law - The number of transistors on integrated circuit chips (1971-2018) Our World in Data Moore's law describes the empirical regularity that the number of transistors on integrated circuits doubles approximately every two years. This advancement is important as other aspects of technological progress - such as processing speed or the price of electronic products - are linked to Moore's law. 50,000,000,000 72-core Xeon Phi Centriq 2400 SPARC M7 GC2 IPU @32-core AMD Epyc IBM z13 Storage Controller Apple A12X Bionic 10,000,000,000 18-core Xeon Haswell-E5 Tegra Xavier SoC Xbox One main SoC Qualcomm Snapdragon 8cx/SCX8180 5,000,000,000 $1-core Xeon Phi "HiSilicon Kirin 980 + Apple A12 Bionic 12-core POWERB "HiSilicon Kirin 710 8-core Xeon Nehalem-EX 10-core Core 17 Broadwell Six-core Xeon 740 8 6 pdragon 835 Dual-core Itanium 20 is Core 17 Broadwell-U Quad-core + GPU GT2 Core 17 Skylake K 1,000,000,000 Pentium D Presler POWER6 got `Quad-core + GPU Core 17 Haswell Apple A7 (dual-core ARM64 "mobile SoC") 500,000,000 9 MB cache Core 17 (Quad) Itanium 2 Madison 6MO Pentium D Smithfield re 2 Duo Conroe Itanium 2 Mckinley Core 2 Duo Wolfdale 3M Pentium 4 Prescott-2MO Core 2 Duo Allendale 100,000,000 `Pentium 4 Cedar Mill AMD K8 Pentium 4 Prescott 50,000,000 Pentium 4 Northwood Barton Pentium 4 Willamette Pentium III Tualatin Atom Pentium II Mobile Dixon AMD K7 . Pentium III Coppermine ARM Cortex-A9 AMD K6-I11 10,000,000 AMD K6 Transistor count Pentium Ill Katmai 5,000,000 Pentium Pro klamath Pentium AMD K5 SA-110 Intel 80486 1,000,000 500,000 TI Explorer's 32-bit Lisp machine chip ARM700 Intel 803860 980 9ARM 3 Motorola 68020 "DEC WRL 100,000 Intel 80286 MultiTitan Motorola 50,000 Intel 80186 Intel 80869 . Intel 8088 OARM 2 "ARM 1 ARM 6 Motorola 650816 10,000 TMS 1000 Zilog 280 6809 NC 4016 DG RCA 1802 65CO2 5,000 Intel 8085 Intel 8008 Intel 8080 Mot torola Technology Intel 4004 1,000 197 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 Data source: Wikipedia (https://en.wikipedia.org/wiki/Transistor_count) The data visualization is available at OurWorldinData.org. There you find more visualizations and research on this topic. Licensed under CC-BY-SA by the author Max Roser.Moore's Law - The number of transistors on integrated circuit chips (1971-2018) Our World in Data Moore's law describes the empirical regularity that the number of transistors on integrated circuits doubles approximately every two years. This advancement is important as other aspects of technological progress - such as processing speed or the price of electronic products - are linked to Moore's law. 50,000,000,000 72-core Xeon Phi Centriq 2400 SPARC M7 GC2 IPU @32-core AMD Epyc IBM z13 Storage Controller Apple A12X Bionic 10,000,000,000 18-core Xeon Haswell-E5 Tegra Xavier SoC Xbox One main SoC Qualcomm Snapdragon 8cx/SCX8180 5,000,000,000 $1-core Xeon Phi "HiSilicon Kirin 980 + Apple A12 Bionic 12-core POWERB "HiSilicon Kirin 710 8-core Xeon Nehalem-EX 10-core Core 17 Broadwell Six-core Xeon 740 8 6 pdragon 835 Dual-core Itanium 20 is Core 17 Broadwell-U Quad-core + GPU GT2 Core 17 Skylake K 1,000,000,000 Pentium D Presler POWER6 got `Quad-core + GPU Core 17 Haswell Apple A7 (dual-core ARM64 "mobile SoC") 500,000,000 9 MB cache Core 17 (Quad) Itanium 2 Madison 6MO Pentium D Smithfield re 2 Duo Conroe Itanium 2 Mckinley Core 2 Duo Wolfdale 3M Pentium 4 Prescott-2MO Core 2 Duo Allendale 100,000,000 `Pentium 4 Cedar Mill AMD K8 Pentium 4 Prescott 50,000,000 Pentium 4 Northwood Barton Pentium 4 Willamette Pentium III Tualatin Atom Pentium II Mobile Dixon AMD K7 . Pentium III Coppermine ARM Cortex-A9 AMD K6-I11 10,000,000 AMD K6 Transistor count Pentium Ill Katmai 5,000,000 Pentium Pro klamath Pentium AMD K5 SA-110 Intel 80486 1,000,000 500,000 TI Explorer's 32-bit Lisp machine chip ARM700 Intel 803860 980 9ARM 3 Motorola 68020 "DEC WRL 100,000 Intel 80286 MultiTitan Motorola 50,000 Intel 80186 Intel 80869 . Intel 8088 OARM 2 "ARM 1 ARM 6 Motorola 650816 10,000 TMS 1000 Zilog 280 6809 NC 4016 DG RCA 1802 65CO2 5,000 Intel 8085 Intel 8008 Intel 8080 Mot torola Technology Intel 4004 1,000 197 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014 2016 2018 Data source: Wikipedia (https://en.wikipedia.org/wiki/Transistor_count) The data visualization is available at OurWorldinData.org. There you find more visualizations and research on this topic. Licensed under CC-BY-SA by the author Max Roser