Ch. 4 Exponential and Log Fncs.
4.1 Exponential Growth/4.2 Exponential Decay
A. OBJ: to graph and use exponential growth and decay.
B. Facts/Formulas:
1. Exponential Fnc: y = a bx or
y = a (1±r)x
2. Exponential Growth: y = a bx-h + k (b>1)
3. Exponential Decay: y = a bx-h + k (0<b<1)
4. Asymptote – a line that a graph gets closer to but never
touches.
5. Domain for Exponential Fncs. is all real numbers.
6. Range for Exponential Fncs. depends on the
horizontal asymptote.
𝑟
7. Compound Interest: A = P(1+ )nt
𝑛
C. Examples:
4.3 Simplify and Graph Functions using “e”
A. OBJ: to simplify and graph expressions with “e”
B. FACTS/FORMULAS:
1. “e” ≈ 2.718
2. Use a calculator to evaluate “e”
3. Use exponent rules to simplify “e”
4. Graphs of “e”: y = aerx
a. If r > 0, then it is an exponential growth
b. If r < 0, then it is an exponential decay
5. Compounded Continuously: A = Pert
C. Examples:
4.4 Evaluate and Graph Logarithmic Fncs.
A. OBJ: to evaluate and graph log fncs.
B. Facts/Formulas:
1. A log fnc. is another way to rewrite an exponential
fnc. : y = bx or bx = y
logby = x
(log base b of y equals x)
2. Special Logs:
a. Common log: log10x = log x
b. Natural log: logex = ln x
3. Inverse Properties:
a. Logbbx = x
b. blogbx = x
c. ln ex = x
d. eln x = x
4. Graphs of Log Fncs.:
a. Domain for Log fnc. depends on vertical
asymptote
b. Range for Log fnc. is all real numbers.
4.5 Properties of Logs
A. OBJ: to rewrite log expressions by using log properties.
B. Facts/Formulas:
1. Product Property: logbmn = logbm + logbn
𝑚
2. Quotient Property: logb = logbm - logbn
𝑛
3. Power Property: logbmn = n logbm
log 𝑎 ln 𝑎
4. Change of Base Property: logba =
=
C. Examples:
log 𝑏
ln 𝑏
4.6 Solving Exp./Log Equations
A. OBJ: to solve both exp./log fncs.
B. Facts/Formulas:
1. Exp. Fncs. must be in the same base.
2. If they cannot be put in the same base, then use logs on
each side.
3. Use log properties to solve log fncs.
C. Examples:
4.7 Write exponential fncs.
A. OBJ: to write exponential and power fncs.
B. Facts/Formulas:
1. Exp. Fnc: y = abx
2. Power Fnc: y = axb