15 Days

One Day

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

 An Exponential Function f with base a

 Sketch Graphs for the following function:

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

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

 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.

 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.

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

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

Two Days

 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?

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

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

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

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

Four Days

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

 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

1) 2) 3) 4)

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

 Begin 4.3.2

Evaluate 1) 2) 3)

 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

 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)

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

 Begin 4.3.3

◦ 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

 Logarithmic Functions Worksheet  pg 59 # 8,  pg , , 20,21  graph 20 & 21(no TI)

One Days

 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)

 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)

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

 Pg 328 #1-15 odd, 18, 20, 22-26

Three Days

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

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

 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?

 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?

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

 Solving Equations Worksheet  Review for Quiz