M3201Ch.6notes.notebook
1
March 20, 2014
M3201Ch.6notes.notebook
2
March 20, 2014
M3201Ch.6notes.notebook
3
March 20, 2014
M3201Ch.6notes.notebook
4
March 20, 2014
M3201Ch.6notes.notebook
5
March 20, 2014
M3201Ch.6notes.notebook
6
March 20, 2014
M3201Ch.6notes.notebook
7
March 20, 2014
M3201Ch.6notes.notebook
8
March 20, 2014
M3201Ch.6notes.notebook
9
March 20, 2014
M3201Ch.6notes.notebook
10
March 20, 2014
M3201Ch.6notes.notebook
11
March 20, 2014
6.3 Solving Exponential EquationsCase One: Bases are equalExample: SolveA) 3x = 33 B) 2x = 24 C) 4x = 43x + 6
M3201Ch.6notes.notebook
12
March 20, 2014
y = 2x 1x y
2
1
0
1
2
3
4
y = 8
Solution:
Case Two: Bases are powers of one anothereg 9 can be written as a power of 3 : 9 = 32
Graphically solve: 2x1 = 8Step one: Write each part of the equation as an equationy = 2x 1 and y = 8
Step Two: Graph both functions on the same axis and find the intersection point.
Algebraically solve: 2x 1 = 8
Step one: Make both sides of the equation have the same base
Step two: Relate the exponents and solve for x
M3201Ch.6notes.notebook
13
March 20, 2014
M3201Ch.6notes.notebook
14
March 20, 2014
Exponential Equations with Radicals:
Remember: is
Solve:
Example: Find the error
M3201Ch.6notes.notebook
15
March 20, 2014
Exponents with fractional bases:
Remember ½ = 21
Example: Solve
Example: Solve the following equations
M3201Ch.6notes.notebook
16
March 20, 2014
M3201Ch.6notes.notebook
17
March 20, 2014
M3201Ch.6notes.notebook
18
March 20, 2014
Problem Solving:Exponential expressions result from the fact that a quantity changes by the same amount each time:• a population doubles each year• a bank account increases by 0.1% annually• a mass of a radioactive element decreases by
half every 462 years
Example:
t 0 1 2 3 4 5
P(t)
What does the value at t = 0 indicate?
How often does the number of trout double?
Solve algebraically
M3201Ch.6notes.notebook
19
March 20, 2014
Halflife problem:
M3201Ch.6notes.notebook
20
March 20, 2014
M3201Ch.6notes.notebook
21
March 20, 2014
M3201Ch.6notes.notebook
22
March 20, 2014
M3201Ch.6notes.notebook
23
March 20, 2014
M3201Ch.6notes.notebook
24
March 20, 2014