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Chapter 7 Exponential Functions

computer chip, Andre Kudyusov/Getty Images
We next consider another important family of functions, called exponential functions. These functions describe growth by a constant factor in equal time periods. Exponential functions model many familiar processes, including the growth of populations, compound interest, and radioactive decay. Here is an example.
In 1965, Gordon Moore, the cofounder of Intel, observed that the number of transistors on a computer chip had doubled every year since the integrated circuit was invented. Moore predicted that the pace would slow down a bit, but the number of transistors would continue to double every 2 years. More recently, data density has doubled approximately every 18 months, and this is the current definition of Moore’s law. Most experts, including Moore himself, expected Moore’s law to hold for at least another two decades.
Year Name of circuit Transistors
\(1971\) \(4004\) \(2300\)
\(1972\) \(8008\) \(3300\)
\(1974\) \(8080\) \(6000\)
\(1978\) \(8086\) \(29,000\)
\(1979\) \(8088\) \(30,000\)
\(1982\) \(80286\) \(134,000\)
\(1985\) \(80386\) \(275,000\)
\(1989\) \(90486\) \(1,200,000\)
\(1993\) Pentium \(3,000,000\)
\(1995\) Pentium Pro \(5,500,000\)
\(1997\) Pentium II \(7,500,000\)
\(1998\) Pentium II Xeon \(7,500,000\)
\(1999\) Pentium III \(9,500,000\)
The data shown are modeled by the exponential function \(N(t) = 2200(1.356)^t\text{,}\) where \(t\) is the number of years since \(1970\text{.}\)