Algebra 2 Ch.8 Notes Page 56 P56 8-2 Properties of Exponential Functions

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

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

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

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)

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 ≈ 2.71828 e comes from y = (1 + 1/x)x e is the asymptote of the function

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?

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)

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.