4.3 Use Functions Involving e Pg. 140

Warm Up – Medicine in the Bloodstream Important Information 85% remains after 1 hour Dosage Natalie 25mg Jason 50mg Derrick 75mg a. Write an exponential equation for the amount of Dimenhydrinate, motion sickness medication, in each astronaut’s bloodstream after “x” hours Natalie Jason Derrick

Warm Up – Medicine in the Bloodstream Important Information 85% remains after 1 hour Dosage Natalie 25mg Jason 50mg Derrick 75mg b. Graph the 3 situations, sketch and label the graphs Don’t forget to change the window!!!!!!

Warm Up – Medicine in the Bloodstream Dosage Natalie 25mg Jason 50mg Derrick 75mg Important Information 85% remains after 1 hour c. Describe the Graphs Similar All Decays Domain Range Differences y – intercepts Steepness “a” – value

Warm Up – Medicine in the Bloodstream Dosage Natalie 25mg Jason 50mg Derrick 75mg Important Information 85% remains after 1 hour d. Find the half-life Half the original concentration (use table) All are 4 to 4.5 hours

Warm Up – Medicine in the Bloodstream Dosage Natalie 25mg Jason 50mg Derrick 75mg Important Information 85% remains after 1 hour e. At what level might you consider each persons bloodstream cleared of medication Natalie - 0.009435 Jason - 0.0098506 Derrick - 0.0098424 This level was used because there was less than thmg in the bloodstream

Warm Up – Medicine in the Bloodstream Important Information 85% remains after 1 hour f. How long did it take the medication to clear each person? Natalie 48.5 hrs Jason 52.5 hrs Derrick 55 hrs The times are different due to the initial amount of medication Dosage Natalie 25mg Jason 50mg Derrick 75mg

4.3 The Natural Base, e

Natural Base, e The natural base, e, is used to estimate the ages of artifacts and to calculate interest that is compounded continuously.

Natural Exponential Function The exponential function with base e, f(x)=ex, is called the natural exponential function. And e is called the natural base. 1 Your calculator has a FANCY ex button you can use!!!  2

Evaluate f(x)=ex to the nearest thousandth for each value of x below: Function Notation x = 2 x = x = 0.25

Exponential Properties Simplify the expression. Exponential Rules Are The Same For Base “e”!! a. = e2 + 5 b. 12 e4 3 e3 = e4 – 3 4 (5 ) c. e –3x 2 = 52 ( e –3x ) 2 = 25 e –6x = 25 e6x

Try This! Simplify the expression. 1. 4. SOLUTION SOLUTION 2. SOLUTION 3. Use a calculator to evaluate SOLUTION SOLUTION 2.117

Homework Green Book!! BK Pg. 142, 2 – 28 Even BK Pg. 143, 2 – 16 Even