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 FUNCTIONX -2 -1 2 4
f(x)
.11
.33 1 9 81
g(x)=3x
(exponential growth!)

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

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

6. 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= r= t= 20 n= 2
P= r= 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. log136a3bc4 log136 + log13a3 + log13b + log13c4
EXPAND THIS LOGARITHM
(using the properties of logarithms)
log136a3bc4
log136 + log13a3 + log13b + log13c4
Product property
log log13a + log13b + 4log13c
Power property

9. 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!)

10. 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

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

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