Exponential Functions and
Equations
Water Temperature – Time vs. Hours
The following table shows the
time, in hours, before the body
of a scuba diver, wearing a
5-millimeter-thick wet suit,
reaches hypothermia (95oF) for
various water temperatures.
Water
Temperature, oF
Time, hours
36
1.5
41
4.8
46
2.6
50
3.1
55
4.9
The following function, which is an example of an
exponential function, closely models the data in the
table: T ( F )  0.1509(1.0639) F
Assignment: Use your calculator to find the exponential regression equation.
Speed of Technology
• In 1965, Gordon Moore, one of the
cofounders of Intel Corporation, observed that
the maximum number of transistors that
could be placed on a microprocessor seemed
to be doubling every 18 to 24 months.
Year
Number of Transistors per
Microprocessor (in thousands)
1971
1979
2.3
3.1
1983 1985 1990 1993 1995
110
280
1998
2000
1200 3100 5500 14,000 42,000
Year
1979
2.3
3.1
1983 1985 1990 1993 1995
110
280
1998
2000
1200 3100 5500 14,000 42,000
Number of Transistors
(in thousands)
Number of Transistors per
Microprocessor (in thousands)
1971
Year
•
•
•
•
When you buy a new computer or smartphone, it will be out-dated within 6 months.
Most recent data points indicate a doubling processing time as short as 12 months.
This would mean that there will be a thousand-fold increase in computational power
in 10 years.
Moore's Law is what chip manufacturers rely on when they decide what sort of chip
to develop in order to remain competitive.
Are We Close to Artificial Intelligence??
The Exponential Growth of Computing Power
Evolution of Data Storage
Important Technology Numbers
Types of Bytes: Data Storage
1 Bit = on / off
1 Byte = 8 Bits
1024 Bits = 1 Byte
1 Kilobyte = 1024 Bytes
1 Megabyte = 1024 KB
1 Gigabyte = 1204 MG
1 Terabyte = 1024 GB
MP3 Players (Storage Space)
Computer Specs (RAM, Memory, Operating System)
2^0
2^1
2^2
2^3
2^4
2^5
2^6
2^7
2^8
2^9
2^10
1
2
4
8
16
32
64
128
256
512
1024