1. REVIEW

2. Exponential Growth Models
When a real-life quantity increases by a fixed percent each year, the amount y of the quantity after t years can be modeled by:
y = a(1 + r)t
a: initial amount
r: percent increase (expressed as decimal)
growth factor: 1 + r

3. COMPOUND INTEREST P = Initial Principal r = annual rate (as a decimal)
n = times per year compounded
t = number of years
What do I put in for “n”?
Quarterly → n = 4
Monthly → n = 12
Daily → n = 365
Yearly → n = 1

4. EXPONENTIAL DECAY MODEL
y = a(1-r)t
Decay Factor: 1-r
a: initial amount
r: percent decrease as a decimal
t: time

5. EXPONENTIAL GRAPHS Exponential Growth Exponential Decay
y = a•bx (b > 1)
y = 3(2)x
y = a•bx (0 < b < 1)
y = 3(0.5)x

6. Continuously compounded interest

7. Definition of a Logarithm with base b
A LOG IS ANOTHER WAY TO WRITE AN EXPONENT
logby = x if and only if bx = y
Logarithmic form: logby = x
Exponential form: bx = y
b and y are positive numbers
b ≠ 0

8. Apply Properties of Logarithms
Section 7.5

9. Properties of Logarithms
Product Property:
Quotient Property:
Power Property:

10. Examples
Expand each expression

11. Expand 6 log 5x3 y 6 log 5x 3 y = 5x 3 y 6 log – = 5 6 log x3 y – + =
EXAMPLE 2
Expand a logarithmic expression
Expand 6
log
5x3 y
SOLUTION 6
log
5x 3 y =
5x 3 y 6
log –
Quotient property = 5 6
log x3 y – +
Product property = 5 6
log x y – + 3
Power property

12. The correct answer is D. Power property Product property
EXAMPLE 3
Standardized Test Practice
SOLUTION –
log 9 + 3log2
log 3 = –
log 9 + log 23
log 3
Power property =
log
( ) 23 –
log 3
Product property =
log 9 23 3
Quotient property = 24
log
Simplify.
The correct answer is D.
ANSWER

13. Change of base formula If a and c are positive numbers with c ≠ 1 Then

14. EXAMPLE 4
Use the change-of-base formula 3
log 8
Evaluate
using common logarithms and natural
logarithms.
SOLUTION
Using common logarithms: =
log 8
log 3
0.9031
0.4771 3
log 8
1.893
Using natural logarithms: =
ln 8
ln 3
2.0794
1.0986 3
log 8
1.893