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.

The following function, which is an example of an exponential function, closely models the data in the table:

Water Temperature, oF

Time, hours

36 1.5

41 4.8

46 2.6

50 3.1

55 4.9

( ) 0.1509(1.0639)FT 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 1971 1979 1983 1985 1990 1993 1995 1998 2000

Number of Transistors per Microprocessor (in thousands)

2.3 3.1 110 280 1200 3100 5500 14,000 42,000

• 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.

Year 1971 1979 1983 1985 1990 1993 1995 1998 2000

Number of Transistors per Microprocessor (in thousands)

2.3 3.1 110 280 1200 3100 5500 14,000 42,000

Year

Num

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f Tra

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(in th

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Are We Close to Artificial Intelligence??

The Exponential Growth of Computing Power

Evolution of Data Storage

Computer Specs (RAM, Memory, Operating System)

MP3 Players (Storage Space)

2^0 12^1 22^2 42^3 82^4 162^5 322^6 642^7 1282^8 2562^9 5122^10 1024

1 Bit = on / off1 Byte = 8 Bits1024 Bits = 1 Byte1 Kilobyte = 1024 Bytes1 Megabyte = 1024 KB1 Gigabyte = 1204 MG1 Terabyte = 1024 GB

Types of Bytes: Data Storage

Important Technology Numbers