1. 15 Days

2. One Day

3.  Exponential functions are those that have  An example of an exponential function is

4.  An Exponential Function f with base a

6.  Sketch Graphs for the following function:

8.  We can shift exponential function using the same patterns from before. Use locator point (0,1).

9. - Both types of reflections will change the position(s) of your intercepts and should be done before shifting.

11.  To solve equations with variables in the exponents we need to:  1. Re-write both sides as the same base using exponent rules.  2. Set the exponents equal using condition 2 of our theorem on exponential functions.  3. Solve for the variable.

13.  Writing an exponential function given the y-int and a point on the function.  1. Substitute the y-int into your equation and solve for b.  2. Re-write your equation with a value for b.  3. Substitute other point into your equation from step 2 and solve for a.  4. Re-write your equation with values for a and b.

14.  Find an exponential function of the form that has the given y-int and passes through the point P

15.  Read 4.1; pg292 (# 2,4,7,9,11b - h, 13,14, 16 - 18, 25 NO TI’s for the graphs)

16. Two Days

18.  You have an account that returns 7% annual interest compounded monthly. If you invest $1500 for a total of 10 years, how much money will you have in the account?

22.  An initial investment of $35000 is continuously compounded at 8.5% interest. How much is the investment worth after 5 years? After 15 years?

24.  Since 1980, world population in millions closely fits the exponential function defined by where x is the number of years since 1980.  The world populations was about 5,320 million in 1990. How closely does the function approximate this value?  Use this model to approximate the population in 2012.

25.  Read 4.2; pg 303 (# 1-7,9,11-13,15,19,21,25)

27.  pg 292 (# 32,37,38,(53 use TI));  pg 304 (# 22,24 (45 & 51 use TI))

28. Four Days

29. 1)3 2 =9 2) x a+b =9 3) 4) The following expressions are equivalent. Examples

30.  The expression above is read “The log of x base a equals y”  x>0 (the number you take a log of must be positive)  If you don’t see an “a” value the base is assumed to be 10. ◦ log 4 = log 10 4  A natural log (ln) has a base of e. ◦ ln 4=log e 4

31. 1) 2) 3) 4)

32.  Pg 317 #1,3,9,11,14(skip e), 17-27 odd.  No TI

33.  Begin 4.3.2

34. Evaluate 1) 2) 3)

35.  Remember that f(x)=log a x and f(x)=a x are inverse functions.  This means that logarithmic functions will look like exponential functions except their x’s and y’s will be flipped. a) Graph f(x)=log 2 x b) Graph f(x)=log 2 (x+2)-1

36.  Domain of f(x)=log x (0,∞)  Range of f(x)=log x (-∞,∞)  Remember you can’t take the log of a negative number or zero.  However… logs can equal negative numbers. Ex: log(1/2)

37.  Pg 317 #4,10,12,16, 33(a-g) No calc  47,59,63,65

38.  Begin 4.3.3

39. ◦ Idea: Rewrite in exponential form. Plug in y’s to find x’s  Graph f(x)=log 4 (2x-1)  Find asymptotes, intercepts, domain and range

40.  Logarithmic Functions Worksheet  pg 59 # 8, 11 - 14  pg 60 1-3, 5 - 17, 20,21  graph 20 & 21(no TI)

41. One Days

42.  Log a (xy)= Log a x+Log a y  Log a (x/y)= Log a x-Log a y  Log a x n = nLog a x  Note: log(x+y) is not equal to log (x)+ log(y)  Note: log(x-y) is not equal to log (x)-log(y)

43.  Log a (xy)= Log a x+Log a y  Log a (x/y)= Log a x-Log a y  Log a x n = nLog a x  Expand Each LogWrite as a single log 1) Log 3 (4x) 2) Ln(3e) 3) Log(2x 3 /y 4 ) 4) 3log(x)+2log(y) 5) ½Ln(4x)-yLn(6) 6) 2ln(xy)-3ln(x)+6ln(y)

44.  Solve 1) Log 4 (2x+4)= 2log 4 3+ log 4 5 2) ln(x)+ln(x+3)=½ln(324)

45.  Pg 328 #1-15 odd, 18, 20, 22-26

46. Three Days

54.  Read 4.5  pg 339 (# 1-3,5,9,10,17,18,20,41,42,45)

56.  pg 340 (# 11,13,15,21,22,25,31,32,43,44,57)

57.  How long does it take for an initial investment of $5000 to grow to $60000 in an account that earns 8.5% interest compounded monthly?

58.  The populations N(t) (in millions) of the United States t years after 1980 may be approximated by the formula.  When will the populations be twice what is was in 1980?

59.  A 100g sample of a radioactive substance has a half life of 30 minutes. After how many hours will 20g remain?

60.  Solving Equations Worksheet  Review for Quiz