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

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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

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 “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)

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

Page 493 2.718 is e

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

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? x is all real numbers What is the range? y > 1 What is the asymptote? f(x) = 2(e)x-2 +1 y = 1

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

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

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 = 618.38 Interest = 618.38 – 500 = 118.38

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