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