CH 8 PORTFOLIO PAGE
Lesson 8-1 & 8-2: Exponential Growth/Decay
Exponential functions are of the form: y = abx
If 0 < b < 1, the graph represents exponential DECAY.
If b > 1, the graph represents exponential GROWTH.
Graph: y = 2x + 3 (table of values)
Compound Interest formula:
A = balance after t years
P = principal
r = rate
n = # times interest is added per
year
t = time in years
Ex 1:How much must you deposit in an account that pays
8% annual interest, compounded monthly, to have a
balance of $1,500 after one year?
r
A  P(1  )nt
n
The Number e
e is an irrational number approximately
equal to 2.71828
Exponential functions with a base of e
are useful for describing continuous
growth or decay.
Continuously Compounded Interest formula
A = amount in account,
P = principal,
r = annual rate of interest,
t = time in years
Ex 2:: Suppose you invest $1,050 at an annual interest rate
of 5.5% compounded continuously. How much will you have
in the account after five years?
A=
Pert
Lesson 8-3: Logarithms
A logarithm is an exponent.
Write the equation in exponential form:
log464 = 3 ___________________
by
logbx = y and
= x are
equivalent expressions
Write the equation in logarithmic form:
24 = 16 _____________________
Evaluate the logarithms:
1)
log 16
2)
4)
5)
2
log39
log497
log225
3)
6)
log88
log31
Lesson 8-4: Properties of Logarithms
PROPERTIES OF LOGARITHMS
Let a, u, and v be positive numbers such that a ≠ 1, and let n be any real number.
Product Property:
Quotient Property:
Power Property:
log a uv 
u
log a 
v
log a u n 
Note: There is no property to simplify the logarithm of a sum.
M. Murray
USE PROPERTIES OF LOGS TO EXPAND AND CONDENSE
Use the properties of logarithms to simplify (condense): (Write as one log expression)
1) 5log3 + 2log2
Use the properties of logarithms to expand:
(Write as a sum or difference of logarithms, or use power property)
2) log45 𝑥
Lesson 8-5: Exponential & Logarithmic Equations
Change of Base formula:
log a x 
log10 x
log10 a
Steps to solve Exponential Equations:
Steps to solve Logarithmic Equations:
1) Isolate power
2) Take log of both sides in same base
3) logaa = x
1) Use properties of logs, if necessary to
condense log expression.
2) Write in exponential form
4) Use change of base formula
Ex) Solve: 3logx – log 2 = 5
Ex) Solve: 2 + 3x = 4
Lesson 8-6: Natural Logarithms
A natural logarithm (ln) is a log with base e. All the same properties of logs also apply to natural
logs.
Simplifying Natural Logarithms:
1) 5 ln 2 – ln 4
2) 3 ln x + ln y
Solve:
3) ln x = -2
4) ex+1 = 30
Simplify using mental math:
3) ln e
4) ln e3
5) ln 1
M. Murray