exponential growth & decay section 4.5 jmerrill, 2005 revised 2008

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Slide 2 Exponential Growth & Decay Section 4.5 JMerrill, 2005 Revised 2008 Slide 3 Review Is this okay? Arguments must be positive Slide 4 Review 500e 0.3x = 600 e 0.3x = 1.2 ln 1.2 = 0.3x x = 0.608 Slide 5 Exponents and Logarithms How are exponents and logarithms related? They are inverses of each other Why is this important? Using inverses allow us to solve problems (we use subtraction to solve addition problems & division to solve multiplication) Many real-life scenarios are exponential in nature and logarithms allow us to solve for the unknown. Slide 6 Examples Using Logarithmic Scales The Richter scale is used to determine the intensity of an earthquake. Measuring acidity using the pH scale, or concentration of ions. Carbon dating. Modeling population growth/decay--just to name a few Slide 7 Exponential Decay Model A(t) = A0ekt A0 is the initial amount K is the growing/decay entity. If k>0, the entity is growing (an increasing function). If k