1. 9x – 7i > 3(3x – 7u) 9x – 7i > 9x – 21u – 7i > – 21u
Warmup Alg 2 14 & 15 February 2012
Solve for i
9x – 7i > 3(3x – 7u)
9x – 7i > 9x – 21u
– 7i > – 21u
i <3 u

2. Agenda Don't forget about resources on mrwaddell.net
Sec 7.3 : Functions w/ e
Euler’s number
A=Pert
Growth and Decay revisited

3. Go over assignment from last class period

4. Section 7.3: Functions w/ Euler’s number, e

5. Exponential equation
“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!

6. A new “Transcendental” Constant
You know about π. π is a constant used in geometry, … e is another constant similar in nature to π. e is equal to … and is called the “Natural Number” (but is good enough)

7. 𝑦=𝑎 𝑒 𝑟𝑥 Exponential equation
If we use e as our constant instead of “b”.
𝑦=𝑎 𝑒 𝑟𝑥
If “r” is positive, it is growth
If “r” is negative it is decay

8. Page 493
2.718 is e

9. Domain and Range
State the domain and range and asymptote of the equation:
D: All real numbers
R: y > 2 and A: y = 2
1. y=2e3x + 2
D: All real numbers
R: y > -4 and A: y = -4
2. y= ½ e-2x -4
D: All real numbers
R: y > -2 and A: y = -2
3. y= .8e4(x+3) -2

10. 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

11. Graphing: domain and range
What is the domain?
x is all real numbers
What is the range?
y > 1
What is the
asymptote?
f(x) = 2(e)x-2 +1
y = 1

12. Graphing: domain and range
What is the domain?
x is all real numbers
What is the range?
y > 4
What is the
asymptote?
f(x) = 3(e)-x+1 +4
y = 4

13. A = Pert $$ equations using e But why have a second A = Amount
formula?
A = Amount
P = Principal
r = rate
It is when the money is
compounded continuously!
t = time

14. Compounding Continuously
If Jose invests $500 in an investment that compounds continuously at 4¼% interest for 5 years, how much interest did he earn?
Are you done?
A = Pert
NO! Read the Question.
A = 500e.0425∙5
A =
Interest = – 500 =
118.38

15. Assignment
Chapter 7.3: 5 – 13, 31 – 38, 47 – 49