Warmup Alg 214 & 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 equationxby )( “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 .
is a constant used in geometry, 3.14159…
e is another constant similar in nature to .
e is equal to 2.718281828459045… and is called the “Natural Number”
(but 2.718 is good enough)
Exponential equationIf we use e as our constant instead of “b”.
If “r” is positive, it is growth
If “r” is negative it is decay
𝑦=𝑎𝑒𝑟𝑥
Page 493
2.718 is e
Domain and RangeState the domain and range and asymptote
of the equation:
1. y=2e3x + 2D: All real numbersR: y > 2 and A: y = 2
2. y= ½ e-2x -4D: All real numbersR: y > -4 and A: y = -4
3. y= .8e4(x+3) -2D: All real numbersR: 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
f(x) = 2(e)x-2 +1
What is the domain?
x is all real numbers
What is the range?y > 1
What is the asymptote?
y = 1
Graphing: domain and range
f(x) = 3(e)-x+1 +4
What is the domain?
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