APC Unit 4 Chapter 5 Review

Review Homework  Any Questions?  Was it harder? Why?  What did you learn?

What to know for the test  Calculator Skills  Natural Log Regressions – lnReg  Understand what the graph should look like  Turn on stat plots  What is x and what is y, L1, L2  Store your regression into y1  P.347 #100  P340 #5

Application of exponential functions  Compounded Interest Rates

Application: Money

Continuous Compounding

Effective Rates – allows us to compare different rates rr

Practice  P. 347 #90  P

Practice  P. 320 #27-30

Growth/Decay Models  y = Ce kt  When t = 0 what is the value of y?  Y = C  C is the original value  What happens to the graph as k increases?  K is the growth rate, k>0  K is the decay rate, k<0

Use the Given information to solve for k  “number of cells doubles every 3 hours”  C is the original amount  When t = 3, y = 2C  Solve for k

Once K is found, solve for other values  “triple” in size  Y = 3C  Solve for t

Building Models from Data  Review: To enter data into a list  (stat), [1: edit]  …enter L2 and L2  To View  (2 nd )(stat plots) >  Look at the data to determine your window  To do the regression:  (stat) > [CALC], [9: LnReg]

Practice Growth Decay Models  P. 346 #87  P. 333 #21

Logistic Model  Define

Solve log/exponential Equations Graphically  Quick  Use Graphing Calculator  Learn from past mistakes  Use ( ) properly  Think about it… does your graph look like a log function? Exponential function?  Check your order of operations  P. 346 #84

Non-Calculator Skills  Composition of functions P , 10, 12  Domain of composed functions  F(g(x)) Exclude where g(x) is undefined  Exclude where f(g(x)) is undefined  (alternately where g(x) is equal to the value that makes f(x) undefined  P  Numerically? #16  Graphically #18, 20

Practice

More Practice

Inverse Functions  How to find?  How to Check/Verify?  F(f -1 (x)) = x and f -1 (f(x))=x  DO NOT JUST FIND THE INVERSE OF YOUR INVERSE  Graphically Reflect over the line y=x  Numerically switch the x and y values  P , 58, 61, 62

Exponential Functions  They’re exponentially FUN  Graph using transformations  Analyze domain and range (use a sketch)

Logarithmic Functions  Graph using transformations  Analyze domain and range (Sketch)

Evaluate (without a calculator)  Exponential expressions  Log expressions  P

Log Rules

Rules and not rules  Lo P even

Solving Equations  Using Inverse operations p , 80  Using substitution to factor p  Using Substitution on Rational  P. 346 #82  Check for extraneous results