Pre Calculus 300
Name _
Applications of Exponential Equations
Date _
Write an equation and show ALL CALCULATIONS for each problem.
1.
In 1947, earthenware jars containing what are known as the Dead Sea Scrolls were
found. Analysis showed that the scroll w
Pre Calculus 300
Name _
Applications of Exponential Equations
Date _
Some common formulas
EXPONENTIAL GROWTH
n ( t ) = n 0e rt
n ( t ) = population at time t
n 0 = initial size of the population
r = relative rate of growth
t = time
RADIOACTIVE DECAY
m( t
Example 1
A ship leaves Port A and travels 130 nautical miles at a bearing of 32 to Port B. It then continues on a bearing
of 122 to its final destination, Port C. Port A is 200 nautical miles from Port C.
Find the distance from Port B to Port C.
What is
Pre Calculus 300
Name _
Change of Base Formula
Date _
Use the change of base formula to evaluate each logarithm. Round to 4 decimal places.
Change of Base:
log b x =
Proof:
log a x
log a b
Start with
y = log b x
Rewrite as an exponential equation:
Take th
Pre Calculus - 300
Name_
Evaluating Logarithms
Date_
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Use the properties of logarithms and the values below to find the logarithm indicated. Do not use a
calculat
Pre Calculus 300
Name _
Introduction to Exponential Equations
Date _
RULE: If the solution to an exponential equation is not obvious ( 3x = 81; x = 4)
Rewrite the exponential equation as a logarithmic equation and solve.
Example 1:
Method #1
(Take the log
Pre Calculus 300
Name _
Solving Logarithmic Equations
Date _
Guidelines:
Isolate the term with the variable, if possible
Compress the logarithm
De log
if the bases are the same set equal to each other
if only one log - write the exponential equation
Solve
Pre Calculus - 300
Name_
Solving Logarithmic Equations Practice #2
Date_
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Solve each equation. Leave solutions in terms of e.
1) log 3 x log 3 5 = log 3 30
2) log
Pre-Calculus - 300
Name_
The Six Trigonometric Functions - Classroom Practice
Date_
6 Y2h0r1z3s FKJustpaL 2ShoxfAtrwWagrVe9 cLOLlCO.U P kAvlolc xrkimgHh6tls5 BrHeysCe1rnvLeedl.t
Find the value of the trig function indicated.
1) csc
2) cot
20
16
12
12
16
Pre Calculus 300
Name _
Review of Exponents and Radicals
Date _
a0 =
a 1 =
1
an
an =
an am =
nm
(a )
a2 a3 =
35
(a )
=
=
23
(3ab ) =
2 3
2
b
3a 2
3 =
b
4 3
b 2
1
2
1
3
a=
4
5
a=
2
7
a=
a=
Simplifying Radicals
n
ab = n a n b
4
1
an = n a
m
an =
2
Pre Calculus 300
Name _
Review of Special Angles
Date _
Find the values without using your UNIT CIRCLE. You may use your UNIT CIRCLE to check
your answers.
1.
Find the angle where tan = 1 and cos > 0 and 2 < < 4 .
2.
Find the 6 trigonometric functions whe
PRECALCULUS 300
CHAPTER 1 SECTION 4
NAME_
REDUCING, MULTIPLYTING, DIVIDING ALGEBRAIC FRACTIONS
REDUCE each of the following to lowest terms:
1.
x 4 y 5
x3y
3.
x 2 10 x + 25
x 2 5x
2.
3x y
y 3x
4.
x4 + x2
x 2 ( x + 1) 2
2.
y2
y
x+2 x+2
4.
3x 2 3
5 x 2 10 x
Pre Calculus 300
Name _
Simplifying Rational Fractions
Date _
Rewrite each division problem as multiplication and simplify
1.
x2
x 2 25 y 2
x
5y x
2.
w 2 + 2w + 1
w +1
3
3.
5 a 2 20
2a + 2
10 a 20
4a
4.
2y
y 4
3
2
y 4y + 4
5.
p2 + 7 p
3p
49 p 2
3 p 21
2
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$
$
$
12#(3&'$43567$8"3&95'#$8"35:9:/#7"3($;&')#*$
$
.&/#$0000000000000000000000000$
$
<&7#$000000000000000$
$
Fill in the values of the angles and the ratio of the lengths of the sides of a 45- 45- 90
and 30-60- 90 right triangle.
$
PRECALCULUS 300
NAME_
CHAPTER 4 SECTION 4
Pages 364-372
DATE_
SOLVING LOGARITHMIC EQUATIONS
Use the properties of LOGARITHMS to find each of the following. COMPRESS each side of the
equation. Solve for x.
Check your answer.
1.
log b x = 3 log b 2 +
1
log
Pre Calculus 300
Name _
The Unit Circle
Date _
Tricks to remembering the Unit Circle
Find the values of each of the trigonometric functions for the specified quadrantal
angles.
Angle
0
90
180
270
360
Radians
Sin Cos Tan Cot Sec Csc