Download 9x – 7i > 3(3x – 7u) 9x – 7i > 9x – 21u – 7i > – 21u i

Warmup Alg 2
14 & 15 February 2012
Solve for i
9x – 7i > 3(3x – 7u)
9x – 7i > 9x – 21u
– 7i > – 21u
i <3 u
Agenda
• Don't forget about resources on
mrwaddell.net
• Sec 7.3 : Functions w/ e
• Euler’s number
• A=Pert
• Growth and Decay revisited
Go over assignment from last
class period
Section 7.3: Functions w/ Euler’s
number, e
Exponential equation
y  (b)
x
“b” can be any positive
number
If “b” is bigger than 1 then it is GROWTH (y
gets bigger)
If “b” is between 0 and 1 then it is DECAY (y
gets smaller)
If the exponent has a “-” sign, then
it is also decay!
A new “Transcendental” Constant
You know about π.
π is a constant used in geometry, 3.14159…
e is another constant similar in nature to π.
e is equal to 2.718281828459045… and is
called the “Natural Number”
(but 2.718 is good enough)
Exponential equation
If we use e as our constant instead of “b”.
𝑦 = 𝑎𝑒
If “r” is positive, it is growth
If “r” is negative it is decay
𝑟𝑥
Page 493
2.718 is e
Domain and Range
State the domain and range and asymptote
of the equation:
D: All real numbers
1. y=2e3x + 2
R: y > 2 and A: y = 2
2. y= ½
3. y=
e-2x
-4
.8e4(x+3)
-2
D: All real numbers
R: y > -4 and A: y = -4
D: All real numbers
R: y > -2 and A: y = -2
Simplifying expressions with e
Simplify the expression:
1.
e2∙e5
1. e7
2.
e2∙e-4
2. 1/e2
3. (3e2)3
3. 27e6
4. (8e9)1/3
4. 2e3
Graphing: domain and range
What is the domain?
f(x) = 2(e)x-2 +1
x is all real numbers
What is the range?
y>1
What is the
asymptote?
y=1
Graphing: domain and range
What is the domain?
f(x) = 3(e)-x+1 +4
x is all real numbers
What is the range?
y>4
What is the
asymptote?
y=4
Assignment
Chapter 7.3:
5 – 13,
31 – 38,
47 – 49