1. Algebra 2
Ch.8 Notes Page 56
P Properties of Exponential Functions

2. Families of Exponential Functions
Parent Function: y = bx
Stretch ( | a | > 1 )
Shrink ( 0 < | a | < 1 ) y = abx
Reflection ( a < 0 )
Translation: y = bx - h + k
(horizontal by h) (vertical by k)
Combined: y = abx - h + k

3. a = .25 Shrink a = 4 Stretch a = 1 Gets Wider Gets Narrower
Graphing y = abx
0 < | a | < 1 Shrink
| a | > 1 Stretch
a = 1
a = .25 Shrink
a = 4 Stretch
Gets Wider
Gets Narrower

4. Reflecting y = abx Graph y = (1/2)2x and y = (-1/2)2x
Label the Asymptote

5. Translating y = abx Graph y = 8 (1/2)x Horizontal Asymptote is y = 0
Shift 2 Units Left and 3 Units Up
Horizontal Asymptote is y = 3
(It shifts Up with the + 3)

6. ex e comes from y = (1 + 1/x)x e is irrational e ≈ 2.71828
Exponential Functions with Base e are useful for describing continuous growth or decay.
e is irrational
e ≈
e comes from y = (1 + 1/x)x
e is the asymptote of the function

7. Continuously Compounded Interest Formula
You invest $1,050 at an annual interest rate of 5.5% compounded continuously. How much money will you have in the account after five years?

8. Half-Life Remember each half-life is 6 hours. (75/6 = 12.5)
The half-life of a radioactive substance is the time it takes for half of the material to decay. A hospital prepares a 100-mg supply of technetium-99m, which has a half-life of 6 hours. Write an exponential function to find the amount of technetium-99m that remains after 75 hours.
Remember each half-life is 6 hours. (75/6 = 12.5)

9. the homework. Also include the homework number.
HW #61
8-2 P442 #2,5,9,12,14,17,19,20,21,23,24,25,39
Please put your name and class period at the top of
the homework. Also include the homework number.