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Ali & Sara!

EXPONENTIAL/LOG. This is Khan Academy Approved !!!. Ali & Sara!. Exponential Growth! f(x)= b x (b > 1). Exponential Decay! f(x)= b x ( 0 < b < 1). SKETCH THE GRAPH OF THIS FUNCTION. g(x)=3 x. (exponential growth!). SKETCH THE GRAPH OF THIS FUNCTION.

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Ali & Sara!

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

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

  3. SKETCH THE GRAPH OF THIS FUNCTION g(x)=3x (exponential growth!)

  4. SKETCH THE GRAPH OF THIS FUNCTION f(x)= 0.5x

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

  6. Interest Formulas! (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

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

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

  9. EXPRESS EACH LOGARITHM IN TERMS OF ln 2 and ln 3 ln 54 ln 9/8 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!)

  10. EVALUATE THIS LOGARITHM log63√36 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

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

  12. CREDITS • Sara’s brain • Ali’s brain • MATHEATRE

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