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 = ae kt . 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 = ab t and Q = ae kt b = e k Annual growth rate Continuous annual growth rate S Butler (Michigan Tech) Chapter 4 Section 2 October 16, 2006 4 / 6
Example Continuous annual Q = ab t Q = ae kt Annual growth rate growth rate 5(1 . 2) t 10 e − 0 . 0943 t -4 S Butler (Michigan Tech) Chapter 4 Section 2 October 16, 2006 5 / 6
Summary 1 Doubling Time & Half-life 2 Conversions between different bases S Butler (Michigan Tech) Chapter 4 Section 2 October 16, 2006 6 / 6
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