6.1 Exponential functions
1. Copy the objective.
2. Copy the definition of an exponential function and
write the general form
3. Write 3 examples of exponential functions
4. Draw the graph in exercise 6.1
6.2 Positive Integer Exponents
1. Copy the objective.
2. For positive integers n explain in CES what xn
means? Give two examples.
3. Define the terms base, exponent, power.
4. Write down the agreement on page 232.
5. Are (2x)3 and 2x3 different, explain.
Example 1. Evaluate 4  32 and (4  3)2
Example 2. Evaluate (-3)3 and -33
Example 3: Evaluate 65 by multiplying by hand, and
then confirm using a calculator.
6.3 Properties of Exponentiation
1. Copy the objective.
Do problems 15-20 on pages 234-235
2. Copy the properties of exponents from page 237.
For each property, give an example of how it works.
Example 1. Simplify (3x3y5)2(4x6)
Example 2. Show by evaluating numerator and
denominator with a calculator that 412/44 = 48
6.4 Rational Exponents
1. Copy the objective.
2. Copy the rule for negative exponents. Give 2
examples
3. Copy the rule for 0 exponents. Give two examples.
Explain in CES how this rule makes sense (hint use the
division of powers rule)
4. Copy the rule for reciprocal exponents. Give two
examples. Explain in CES how this rule makes sense
(Hint: use the multiplication of powers rule)
5. Copy the rule for fractional exponents. Give 2
examples. Explain in CES how this rule makes sense
(Hint: use the multiplication of powers rule and the
reciprocal exponents rule)
Example 1. Show that 1222/3 is the same as (1221/3)2 Do
both with a calculator which will take square roots.
Example 2. Evaluate 4 256.57 using the definitions of
reciprocal exponents and a calculator.
2
(4 x 3 y 6 z 2 ) 4
Example 3. Simplify
12 x 3 y 4 z 2
6.5 Powers of Radicals w/o Calculators
1. Copy the objective.
Example 1. Evaluate 2563/4
Example 2. Evaluate 17285/3
Example 3. 5 243  3 81
6.6 Scientific Notation
1. Copy the objective.
2. Define characteristic in scientific notation
3. Define mantissa in scientific notation
4.Copy description of scientific notation form on p.254.
Example 1: Write in scientific notation
a. 4566839205867
b. 0.000000034567
Example 2: Multiply (4x1012) (6x10-22)
Write the answer in scientific notation
6.8 Solving by Logarithms
1. Copy the objective.
2. Copy definition of base 10 log. Give 2 examples.
3. Copy the property of a logarithm of a power of 10.
Example 1. Solve and check 10x=372
Example 2. 34x10-0.3x=59
Example 3. Solve and check 7x= 271
6.9 Logarithms with other bases
1. Copy the objective.
2. Copy definition of base b log. Give two examples.
3. Write the names of y, b, and x in the following
equation y  log b x
Example 1. Find x if log5 x  17
Example 2. Find x if log6 81  x log381=
4
Example 3. Find x if log x 7 
5
6.10 Properties of Logarithms
1. Copy the objective.
Work problem 6-9#46 before reading
2. Copy the property of the log of two (or more)
factors.
3. Copy the property of the log of a quotient.
4. Copy the property of the log of a power.
Example 1: Given the log 2 = .301 and log 3 =.477,
find an approximation for the log of 108 without using
a calculator log key.
Example 2: Express log12 8  log12 6 as a sungle
logarithm of a single argument.
Example 3: Solve 6x=92 by taking the log of each
member and using the log of a power property.
6.11 Proofs of Log Properties
1. Copy the objective.
Example 1: Find a decimal approximation for log338
2. Copy the change of base property for logarithms.
Example 2: Prove that
logb(x/y) =logbx - logby
6.12 Inverses of Functions
1. Copy the objective.
2. Copy the definition of an inverse of a function and
given an example of a function and its inverse.
3. What is the standard notation for the inverse of a
function?
4. What is the most striking feature of a function and
its inverse?
Example 1: If f(x) = 6x+4.5 sketch the function and
its inverse and tell whether the inverse is a function.
Example 2: Invert f(x) = x2+3x-4 and sketch the two
graphs. Is the inverse a function?
6.13 Add-Multiply Property of Exponential
Functions
1. Copy the objective.
2. Write the general equation for an exponential
function.
3. Write the add-multiply property of exponential
functions and its proof.
4. Write the add-add property of linear functions and its
proof.
5. Write the multiply-multiply property of a variation
function and its proof.
6. y=logx is a logarithmic function. Is there a property
for this function?? Show me.
Example 1: Suppose that f(x) varies exponentially with
x and f(2)=300 and f(6) = 200. Calculate values of f(x)
and use the information to draw the graph.
Example 2: Which of the following functions f or g
could be an exponential function and why is the other
one not an exponential function?
x
f(x)
g(x)
2
76.4
93.1
5
62.7
76.405
8
51.457 58.773
11
42.23
44.525
If the domain of this function is 0<x<20, what is f(7)
6.14 Mathematical Models
1. Copy the objective.
2. Write the standard forms for equations linear,
quadratic, and exponential, variation (direct and
inverse) and logarithmic.
Example 1: Problem 1 page 303.