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Natural Logarithms Section 8.6 Recall that e 2.718... Natural Logs ln loge ln 1 = loge 1 ? Evaluate 1. ln e 3 2. ln e 2 3. ln e 5 log e 4. 2 5. ln 5 Using Natural Logs to solve equations. 1. 7e 2 23 2x x 3 2. e 5 10 How long would it take an investment to double if it is compounded continuously at 3.25%? A Pe rt Solving Natural Log Equations 1. ln 3x 27 x 1 2. ln 5 3 Solving Natural Log Equations 3. ln x 2 ln 3 4 1 3 4. ln 5x 3 2 Write an exponential equation then solve 1. Carbon-14 is used to study fossil remains. It has a half-life of 5760 years. What is the age of a fossil with 1/5 of its carbon-14 remaining? 2. Medical research indicates that the risk of having a car accident increases exponentially as the concentration of alcohol in the blood increases. The risk is modeled by: R= , where x is the blood alcohol concentration and R, given as a percent, is the risk of having a car accident. What blood alcohol concentration corresponds to a 17% risk of a car accident? 3. The exponential decay model for Carbon-14 is y ne .000121t Prehistoric cave paintings were discovered in a cave in France. The paint contained 15% of the original carbon14. Estimate the age of the paintings. Homework Workbook 8-6 #7-45 odd Wkst: word problems Page 465 #14-38