Chapter 4 Section 2 MA1032 Data, Functions & Graphs Sidney - - PowerPoint PPT Presentation

Chapter 4 Section 2

MA1032 Data, Functions & Graphs Sidney Butler

Michigan Technological University

October 16, 2006

S Butler (Michigan Tech) Chapter 4 Section 2 October 16, 2006 1 / 6

Exercise #32

In 2001, the Internet was linked by a global network of 147 million host

• computers. The number of host computers has been growing

approximately exponentially and was about 1.3 million in 1992.

1 Find a formula for the number, N, of internet host computers as an

exponential function of t, the number of years since 1992, using the form N = aekt.

2 What is the continuous annual percent increase? 3 What is the doubling time? S Butler (Michigan Tech) Chapter 4 Section 2 October 16, 2006 2 / 6

Exercise # 36

The half-life of iodine-123 is about 13 hours. You begin with 50 grams of iodine-123.

1 Write an equation that gives the amount of iodine-123 remaining

after t hours.

2 Determine the number of hours needed for your sample to decay 10

grams.

S Butler (Michigan Tech) Chapter 4 Section 2 October 16, 2006 3 / 6

Conversion between Q = abt and Q = aekt

b = ek Annual growth rate Continuous annual growth rate

S Butler (Michigan Tech) Chapter 4 Section 2 October 16, 2006 4 / 6

Example

Continuous annual Q = abt Q = aekt Annual growth rate growth rate 5(1.2)t 10e−0.0943t

• 4

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Summary

1 Doubling Time & Half-life 2 Conversions between different bases S Butler (Michigan Tech) Chapter 4 Section 2 October 16, 2006 6 / 6