VIEWS: 24 PAGES: 3 POSTED ON: 11/10/2010
Exponential Functions An exponential pattern is something that grows or decays by a multiple of some number. For example, something that doubles, multiplies by 2 every time, and something that triples, multiplies by 3 every time. The general exponential equation is y = a(b)x, where a is the starting point (the number at zero) and b is the number you are multiplying by. If b is bigger than 1, the equation is growth, and if b is less than 1, the equation is decay. Ex: x y x y The starting point 0 2 The starting point 0 16 1 6 1 8 Multiplying by 3 Dividing by 2…so, multiplying by ½ 2 18 2 4 3 54 3 2 This one’s growth This one’s decay y = 2(3)x y = 16(½)x When dealing with percentage growth or decay, like interest problems or population problems, the general formulas are: Growth: A = P(1 + r)t A = Final amount P = Initial amount Decay: A = P(1 – r)t r = rate (in decimal form) t = time in years Ex: 1. In 1800, Sallie Mae just found out that one of her ancestors invested $300 in a savings account that paid 4% interest annually. Find the account balance after the year 1950. P = $300 Equation A = 300 (1 + 0.04)150 r = 0.04 using a calculator, typing in 300(1+0.04)150 t = 150 the account balance is $107676.80 2. Suppose the acreage of forest is decreasing by 4% every year because of development. If there are currently 6,000,000 acres of forest, determine the amount of forest left after 15 years. P = 6000000 Equation A = 6000000(1 – 0.04)15 r = 0.04 using a calculator, typing in 6000000(1 – 0.04)15 t = 15 the forest acreage is 3,252,518.28 acres Practice Problems 1. y = 8(1.04)x a) What is the initial amount? b) What is the growth factor? 2. y = 7(0.43)x a) What is the initial amount? b) What is the decay factor? 3. x y 1 1 a) What is the initial amount? 2 4 b) What is the growth factor? 3 16 4 64 c) What is the equation? 5 256 4. x y 1 81 a) What is the initial amount? 2 27 b) What is the decay factor? 3 9 4 3 c) What is the equation? 5 1 Use the following tables to answer the questions #5 - 6. A) x y B) x y C) x y D) x y 1 1 1 2 1 1 1 1 2 0.5 2 8 2 11 2 4 3 0.25 3 18 3 21 3 16 4 0.125 4 32 4 31 4 64 5. Which table represents an exponential growth function? 6. Which table represents an exponential decay function? 7. Write an equation that represents the data in the table. x 1 2 3 4 5 y 75 30 12 4.8 1.92 8. Write an equation that represents the data in the table. x 0 1 2 3 4 y 3.125 6.25 12.5 25 50 9. For California, the population in 1900 was 1.77 million. Since then, the population has grown at a rate of 3% per year. According to this rate, what was the population in 2000? 10. A $55,000 purchase depreciates at 16% each year. What would the value be after 10 years? Answers 1. a) 8 b) 1.04 2. a) 7 b) 0.43 3. a) ¼ (remember it’s where x= 0) b) 4 c) y = ¼ (4)x 4. a) 243 b) 1/3 c) y = 243 (1/3)x 5. D 6. A 7. y = 187.5(.4)x 8. y = 3.125(2)x 9. The population in 2000 was 34016978.61 people 10. The value is $9619.57