Stare at this image…. Do you see the invisible dots?

Example #6 Determine the amount of an investment if $1000 is invested at an interest rate of 4% compounded semi-annually for 5 years. P(1 + ) n r n t A = 1000 (1 + ) (5) A = A = 1000(1.02) 10 A = $

Warm-Up The number of students at West Ottawa High School in 1992 was Since then, the number has increased 3.2% each year. If this continues, how many will there be in 2012? y = b(1 + r) x y =1280(1 + ) y = 1280(1.032) 20 y = 2403

Homework Answers 9.C = 18.9( ) t 10.≈ million computers 11. W = 43.2( ) t 12. ≈ million people 13. ≈ 122,848,204 people 14. ≈ $ ≈ $14, About 17,125,650 visitors 21. ≈ %

Lesson 10-6 B Objective: Solve problems involving exponential decay

Percentage Decay Formula y = b = initial amount r = % decay (as a decimal) x = time b (1 - ) x r

Words that mean decay (get smaller): Depreciates Decrease Less

Example # 1 In 2004, the population of Australia was decreasing by 0.8% each year… (a)Find the growth factor, a. (b)The 2004 population was 17,800,000. What is the projected population for the year 2010? y = b ( 1 – r ) x y = ( 1 – )17,800, y = ( )17,800,000 6 (a)(b) ,962,507

Example # 2 You bought a car for $28,500 in What is the value of the car in 2008 if it depreciates at 13% each year? y = b ( 1 – r ) x y = ( 1 – )28, y = ( 0.87 )28,500 3 $ 18, 767

Half-Life Formula The half-life of a compound is a measurement of how long it takes for one half of the compound to break down. The formula for half-life looks like this: y = b (.5 ) x b = Initial Amount of the Compound x = Number of Half-Life Periods *** NOT the Half-Life ***

Example # 3 An isotope of Cesium-137 has a half-life of 30 years. If you start with 20 mg of the substance, how many mg will be left after 90 years? How many after 120 years? y = b (.5 ) x y = (.5 )20 3 y = (.5 )20 4 y = 2.5 mg y = 1.25 mg = 3 half-lives! = 4 half-lives!

Example # 4 Radium-226 has a half-life of 1,620 years… (a)Write an equation for the amount of Radium remaining if you start with 100 mg and x number of half-lives have passed. (b)If you begin with 4 mg, how much will be left after 3 half-lives? y = b (.5 ) x y = (.5 )4 3 (a) (b) y = 100(.5) x 0.5 mg

Assignment: Page 563, problems 1, 3, 16, 17, 19, 20, 23, 24 Quiz Friday