EXPONENTIAL/LOG This is Khan Academy Approved!!! Ali & Sara!

Exponential Growth! f(x)= bx (b > 1) Exponential Decay! f(x)= bx ( 0 < b < 1)

SKETCH THE GRAPH OF THIS FUNCTION X -2 -1 2 4 f(x) .11 .33 1 9 81 g(x)=3x (exponential growth!)

SKETCH THE GRAPH OF THIS FUNCTION x -2 -1 2 4 f(x) 1 .25 .0625 f(x)= 0.5x

The Number “e” which is used for…..                    

Interest Formulas! EXAMPLES… A= 1000e0.08*10 A= 300(1+0.06/2)2 *20 (compounded n times per year) (compounded continuously) EXAMPLES… Krysti invests three hundred dollars in an account with a 6% interest rate, making no other deposits or withdrawals. What will Krysti’s balance be after twenty years if interest is compounded semi-annually? If one thousand dollars is invested in an online savings account, earning 8% per year, compounded continuously, how much will be in the account after ten years? P= 300 r= 0.06 t= 20 n= 2 P= 1000 r= 0.08 t=10 A= 1000e0.08*10 A= 300(1+0.06/2)2 *20 (simplify!) (simplify!) A= 1000e0.8 A= 300(1+0.06/2)40

Properties of Logarithms Product Property! logbxy= logbx + logby Quotient Property! log b— = logbx ­ logby Power Property! logbxP= p logbx x y

log136a3bc4 log136 + log13a3 + log13b + log13c4 EXPAND THIS LOGARITHM (using the properties of logarithms) log136a3bc4 log136 + log13a3 + log13b + log13c4 Product property log136 + 3log13a + log13b + 4log13c Power property

ln 54 ln 9/8 EXPRESS EACH LOGARITHM IN TERMS OF ln 2 and ln 3 ln 2 x 27 ln 32 / 23 ln 2 x 33 ln 32 – ln 23 ln 2 + ln 33 ANSWER: ln 2 + 3ln 3 ANSWER: 2ln 3 – 3ln 2 (this is the product and the power property!) (this is the quotient and the power property!)

EVALUATE THIS LOGARITHM flip the cube root into a power log6(36)1/3 rewrite 36 to 62 to have a form that can be canceled out log6(62)1/3 multiply 2 x 1/3 log6(6)2/3 cancel  log6(6)2/3 ANSWER: 2/3

JUST A LITTLE TRICKERY… CIRCLE METHOD log8x = 4 HOW IT WORKS: One to One property of Exponential Functions! x = 84  

CREDITS Sara’s brain Ali’s brain MATHEATRE