1. 4.3 Use Functions Involving e
Pg. 140

2. 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

3. 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!!!!!!

4. 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

5. 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

6. 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
Jason
Derrick
This level was used because there was less than thmg in the bloodstream

7. 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 hrs
Jason hrs
Derrick 55 hrs
The times are different due to the initial amount of medication
Dosage
Natalie 25mg
Jason 50mg
Derrick 75mg

8. 4.3 The Natural Base, e

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

10. 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

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

12. 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

13. Try This! Simplify the expression. 1. 4. SOLUTION SOLUTION 2. SOLUTION3.
Use a calculator to evaluate
SOLUTION
SOLUTION
2.117

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