R—05/28/09—HW #73: Pg 477:47,49,50; Pg 490:17,49-61odd; Pg 496:31-55 eoo; Pg 505:25-59 odd 50) V=22000(.875)^t; 14,738

F—05/29/09—HW #74: Pg 469: 19-24; Pg 477: 19-24; Pg 496: eoo; Pg 505: even 20) E22) A24) D 20) E22) B24) A 26) -1\528) no sol30) ln(1\6)32) (ln 3)\5 34) ln 5\336) ) (ln5.5)\440) ln ) log25544) 1\246) e^(15\8)48) e^(5\2) 50) 1552).72954) 25656) no sol 58) no sol

Chapter 8 Review

An exponential function involves y = b x where the base b is positive and not equal to 1. An asymptote is a line the graph approaches. Usually represented by a dotted line An exponential growth function is when b > 1 An exponential decay function is when 0 < b < 1 Tell me if the following are growth or decay functions. Decay Growth Decay

One to Review 1) Find key points 2) Add ‘h’ to the x-value 3) Multiply ‘a’ to the y-value 4) Add ‘k’ to the y-value Other info to find: y – intercept: Asymptote: Domain: All real numbers Range: End behavior: x  ∞; f(x)  _____ x  -∞; f(x)  _____ h = 1 a = 2 k = -2

A town of 5000 grows at a rate of 10% per year. How many people are in town after 10 years? y = a(1 + r) t y  final value a  starting value r  % increase, in decimal form (1 + r)  Growth Factor t  Time Find the info Write equation Answer question y = (1 + ) Calculator Plug – In 5000 * (1.1)^ people (answers must make sense)

A car that costs 25,000 depreciates at a rate of 5% per year. A) What is the value of the car after 7 years? B) When is the car worth $20,000? Calculator – Windows and Intersect y = a(1 – r) t a  r  Decay factor  t 

You can treat it like a number.

Let b and y be positive numbers, and b = 1. The LOGARITHM of y with base b is log b y and is defined as log b y = x if and only if b x = y You read this log base b of y equals x.

Rewrite in Exponential Form

Log Properties: g(x) = log b x is the inverse of f(x) = b x That means g(f(x)) = log b b x = x, and f(g(x)) = Try to make things match up with the base, and it’ll work out ok.

Finding inverses A) Simplify first 1) Switch x and y 2) Change forms 3) Simplify

Finding inverses A) Simplify first 1) Switch x and y 2) Change forms 3) Simplify

General Solving Rules Methods of solving –Make bases of exponents the same Notice when both sides have x as an exponent, and it looks like you can make bases the same. –Log both sides Generally if you have a variable exponent on only one side. Make the base of your log the same as the base of the exponent –Make terms inside logs equal Both sides of the equation have logs with same bases May involve condensing log expressions –Exponentiating both sides One side has a log, one side doesn’t May involve condensing log expressions –NEED TO DOUBLE CHECK!!!!

CAN’T HAVE NEGATIVE INSIDE OF LOGS! EXTRANEOUS SOLUTION. MUST ALWAYS DOUBLE CHECK!!!!!

Exponentiating both sides

MUST ALWAYS DOUBLE CHECK!!!!!

R—05/28/09—HW #73: Pg 477:47,49,50; Pg 490:17,49-61odd; Pg 496:31-55 eoo; Pg 505:25-59 odd F—05/29/09—HW #74: Pg 469: 19-24; Pg 477: 19-24; Pg 496: eoo; Pg 505: even