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Warmup Alg 2 1 4 & 15 February 2012

Warmup Alg 2 1 4 & 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=Pe rt Growth and Decay revisited.

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Warmup Alg 2 1 4 & 15 February 2012

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  1. WarmupAlg 214 & 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 . • 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)

  7. Exponential equation If we use e as our constant instead of “b”. 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. e7 1. e2∙e5 2. 1/e2 2. e2∙e-4 3. 27e6 3. (3e2)3 4. 2e3 4. (8e9)1/3

  11. Graphing: domain and range What is the domain? x is all real numbers What is the range? y > 1 What is the asymptote? y = 1 f(x) = 2(e)x-2 +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? y = 4 f(x) = 3(e)-x+1 +4

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

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