1. Exponential Equations and LOG’s f(x) = y = a x Log a {y} = x Log 10 {y} / Log 10 {a} = x

2. Objectives: Exponential Functions: f(x)= a x Graph Evaluate Solving DO NOW: 3 minutes f(x)= x 2 + 4x +4 GraphVertex Domain=__Range= ___ X interceptY intercept  IN CLASS pg 276-78 E1-3  Evaluate f(4)  f(x) = 2 x  f(x)= (½) x  f(x) = 2 -x  f(x) = 2 (x – 3)  Graph  f(x) = 2 x  f(x)= (½) x  f(x) = 2 -x  f(x) = 2 (x – 3)  Page 283 Ex 6 – 7  Page 287  #’s 1 – 10 all  Lesson 1 HOMEWORK:  Page 287  #’s 1 – 10 all  Page 288  #’s 13, 17, 23, 25, 30, 39,43, 45, 49, 55, 61, 62, 67  HONORS  23, 30, 48, 50, 55, 61, 71,73, 77, 87,89, 91 Unit 4 Lesson 1 4.1 Nov 30

3. Laws of Exponents  (x p *x q ) = (x p +q )  (2 3 ) * (2 2 ) = (2 5 ) = 32  (x p / x q ) = (x p - q )  (2 3 ) / (2 2 ) = (2 3-2 ) = 2  (x p ) q = (x p * q )  (2 3 ) 2 = (2 6 ) = 64  (x -p ) = 1 / (x p )  (2 -3 ) = {1 / (2 3 )} = (1/8) = 0.1250  (x p/q ) = ({ q √(x) } p )  (16 3/4 ) = ({ 4 √(16) } 3 ) = (2) 3 = 8 Unit 4 Lesson 1 4.1

4. Laws of LOG’s  log b M*N = log b M + log b N  log b M/N = log b M – log b N  log b M N = (N)* log b M  Solving for the EXPONENT  a X = Y  Since we only have  log 10  log e = Ln  USE Change of Base Formula  a X = Y   log a (Y) = X  Log a (Y) = X   X = Log a Y = log 10 (Y) / log 10 (a) Unit 4 Lesson 1 4.1

5. Objectives: Solve Compound Interest Problems Solve Continuous Compound with “e” Solve {Radioactive} Decay DO NOW: Graph f(x) = 2 (x – 3) Find f(2) =  IN CLASS  Page 285 -286  Examples 8, 9, 10  Lesson 2 HOMEWORK  Page 289  #’s 93 – 103 Odd  #’ 102  HONORS DEC 5 th  #’s 93 – 103 Odd  #’ 100, 102, 104. 105, 108, 109 Unit 4 Lesson 2- 4.1 Dec 2/5 Page 284 Compound Interest A(t) = P 0 *(1 + r/n) nt Page 286 Radioactive decay {r is Negative} A (t) = A 0 e rt Page 286 Continuous Compound {r is Positive} A (t) = P 0 e rt Half Life N(t) = N (0) * (1/2) t/h

6. DO NOW: Page 289 #100  IN CLASS  Page 293-4  Examples 1 – 4  Page 297-8  Examples 6 – 9  Page 299  Function Gallery Unit 4 Lesson 3 4.2 Dec 5-6 Objectives: Solve logarithmic functions Graph logarithmic functions  Lesson 3 HOMEWORK:  Page 300  #’s 1 – 10 all  Page 301  #’s 13, 17, 23, 25, 30, 31,33, 35, 51, 55, 59, 62, 67  HONORS  Page 301  #’s 23, 30, 48, 50, 55, 61, 71,73, 77, 87,89, 91

7. Objectives: Solve logarithmic WORD PROBLEMS DO NOW: If cancer cells grow according to the equation: N(t) = N 0 e rt If the rate of growth is 0.00464 / hour If the N 0 = 1 cell How many cells will be produced in a day ( 23.9659 hours) How long will it take (t) to produce 4 X 10 6 (“fatal”) cancer cells  IN CLASS  Page 302  #’s 103, 107, 111, 113  Lesson 4 HOMEWORK  Page 302  #’s 103, 107, 111, 113  116, 117, 118, 121, 122  HONORS  Page 302  #’s116, 117, 118, 121, 122,  125, 126, 128, 131 Unit 4 Lesson 4 Jan 3 Review Continuous A(t) = P 0 e rt Decay {r is Negative} Compound {r is Positive}

8. Objectives: REVIEW: Rules of Exponents and Logarithms Exponential Growth and Decay DO NOW: (2 3 ) * (2 2 ) = (2 3 ) / (2 2 ) = (2 3 ) 2 = (2 -3 ) = (16 3/4 ) =  IN CLASS  Rules for Logs Page 309  log b M*N = log b M + log b N  log b M/N = log b M – log b N  log b M N = (N)* log b M  Solving for the EXPONENT  a X = Y  Since we only have  log 10 = loglog e = Ln  USE Change of Base Formula  a X = Y  log a (Y) = X  Log a (Y) = X  X = Log a Y  X= log 10 (Y) / log 10 (a)  Lesson 5 In Class / HOMEWORK  Page 288  #’s 17, 25, 45, 49, 61  Page 289  #’s 95, 99, 103  Page 301  #’s 13, 23, 31, 35, 55, 59, 67  Page 302  #’s 103, 107,113, 117, 121 Unit 4 Lesson 5 Jan 6 4.2

9. Objectives: REVIEW Solve Compound Interest Problems Solve Continuous Compound with “e” Solve {Radioactive} Decay Unit 4 Lesson 5 Continued Page 284 Compound Interest A(t) = P 0 *(1 + r/n) nt Page 286 Radioactive decay {r is Negative} A (t) = A 0 e rt Page 286 Continuous Compound {r is Positive} A (t) = P 0 e rt Half Life N(t) = N (0) * (1/2) t/h KNOW THESE FOUR BASIC FORMULA’s

10. Objectives: Rules of Logarithms DO NOW: 10 Min Page 305 Modeling US Population Part (a)  IN CLASS  Review Homework  Page 304 #’s 1, 5, 7, 8, 9  Q  Page 305 Modeling US Population  Lesson 6 HOMEWORK  Finish the page 305 Model  What will the population be  in 2012?  In 2020? Unit 4 Lesson 6 Jan 9 4.2

11. Objectives: Using Rules of Logs Page 309 DO NOW: Solve for x 3 x = 7 Log 7 / log 3 = 1.7712  IN CLASS  Page 306 -309 Example Problems 1 – 4  Page 310-311 Example Problems 5 – 8  (x9) How long would it take to double an initial investment of $2,500 at 6% compounded daily (n=365)?  (x10) What is the annual investment rate r, compounded monthly (n = 12) that $1,000 would grow into $3,500 in 20 years?  Lesson 7 In Class-HOMEWORK  Page 314: # 1- 9 ODD  Page 314 - 315:  #’s 1, 7, 11, 23, 35, 59 – 71 ODD Unit 4 Lesson 7 4.3

12. Objectives: Practice with Logs and Exponents DO NOW: Solve for x 7 x = 3 Log 3 / log 7 = 0.56458  IN CLASS  Page 317 Pop Quiz 1 – 7 ODD  Page 315 – 317:  #’s 81, 85, 89, 91, 93,94, 100  Lesson 8 HOMEWORK  Page 315 – 317:  #’s 81, 85, 86, 88, 89, 90, 91, 93,94, 100  HONORS 101 Unit 4 Lesson 8 4.3

13. Objectives: KNOW THESE Formulas Find ages using Half Life formula(s) N(t) = N (0) * (1/2) t/h Find times using Newton’s Cooling formula(s) D (t) = D 0 e kt Find Pay off times for Mortgage and loans R = R 0 {(r/n) / [1 – (1 + (r/n) (-nt) ] DO NOW: The fatal number of Hepatitis viruses in human body is 100,000. Find how long it will take for a patient to succumb if not treated when the initial number of viruses was 1,000 and they continuously reproduce at a rate 10% per day? A (t) = A 0 e rt 100,000 = 1000 (e) (.1*t) 1000 = e (.1t) Ln (1000) / Ln(e) =.1t 6.9078 / 1 =.1t 69.078 days = t  IN CLASS  Page 322 – 324  Example Problems 5,6,7  Page 326-27 :  #’s 59 – 69 odd 73  Lesson 9 HOMEWORK  Page 326-27 :  #’s 59 – 69 odd 73  HONORS #66, # 68 Unit 4 Lesson 9 4.4

14. Objectives: More Practice with Formula’s DO NOW: Go Over homework with Table mates Q  IN CLASS  Page 328 – 329:  #’s 75, 76, 79, 82,83, 84, 85, 89  Lesson 10 HOMEWORK  Page 328 – 329:  #’s 75, 76, 79, 82,83, 84, 85, 89 Unit 4 Lesson 10

15. Objectives: Review for Test DO NOW: Go Over homework with Table mates Q  IN CLASS  Page 333  #’s 55 – 62 ALL  BY TEAM  Page 336  #’s: 1 – 21 ALL  Lesson 11 HOMEWORK  Summary Sheet  Exponent Rules  Log Rules  Solving for exponent  Utilize decay and growth Formula’s  Continuous  Periodically  Utilize Half Life Formula’s  Find times using Newton’s Cooling formula(s)  Find Pay off times for Mortgage and loans  TEST tomorrow Unit 4 Lesson 11

16. Unit 4 Logs TEST Homework: Chapter Five VOCAB Page