Lesson 4.6 1. Shan Shannon's car s new car sold for $28,000. Her online research indicates that the car will depreciate at a rate of 5.25% per year, write the exponenti al depreciation formula for 2,00(325) 28,000 (I-.05 2. Lui year sa purch ased a used car for D dollars. The car depreciates exponentially at a rate of E% per a) Write an expression for the value of the car in 5 years. b) Write an expression for the value of the car in A years. D(1-E c) Write an expression for the value of the car in M months. 3. The historical prices of a car are recorded for 11 years as shown. Age Value (S) Age Value (S) 0 19,000 6 8,600 7 7,200 2 13,700 8 6,900 3 12,000 9 6,000 4 10,500 10 5,600 116,325 9,700 a) Determine the exponential depreciation equation that models this data. Round to the nearest hundredth. y # la,ooo ( l-r ) b) Determine the depreciation rate. Show your work. c) Predict the value of this car after years. Show your work. 4. When sold as a new car in the 1950s, the price of a specific classic car was $13,074.It depreciated in value over the next few years. Then, in 1977, something interesting began to happen, as seen in this table of values YearValue 1977 1987 $6,500 $10,500 a 1997 $22500 $47,800 $94,000 2007 2017 a) What happened to the value of the car? Why do you think this happened? The value op the Car went up or appreciated b) Let 1977 be Year 1, 1987 be Year 11, 1997 be Year 21, and so on. Find an exponential growth equation that models this situation. Round the numbers to the nearest hundredth. c) Does this scenario provide a depreciation rate or appreciation rate? How do you know? d) What is the value of the rate to the nearest hundredth of a percent? (Hint: A rate will never be negative.) Lesson 4.6 1. Shan Shannon's car s new car sold for $28,000. Her online research indicates that the car will depreciate at a rate of 5.25% per year, write the exponenti al depreciation formula for 2,00(325) 28,000 (I-.05 2. Lui year sa purch ased a used car for D dollars. The car depreciates exponentially at a rate of E% per a) Write an expression for the value of the car in 5 years. b) Write an expression for the value of the car in A years. D(1-E c) Write an expression for the value of the car in M months. 3. The historical prices of a car are recorded for 11 years as shown. Age Value (S) Age Value (S) 0 19,000 6 8,600 7 7,200 2 13,700 8 6,900 3 12,000 9 6,000 4 10,500 10 5,600 116,325 9,700 a) Determine the exponential depreciation equation that models this data. Round to the nearest hundredth. y # la,ooo ( l-r ) b) Determine the depreciation rate. Show your work. c) Predict the value of this car after years. Show your work. 4. When sold as a new car in the 1950s, the price of a specific classic car was $13,074.It depreciated in value over the next few years. Then, in 1977, something interesting began to happen, as seen in this table of values YearValue 1977 1987 $6,500 $10,500 a 1997 $22500 $47,800 $94,000 2007 2017 a) What happened to the value of the car? Why do you think this happened? The value op the Car went up or appreciated b) Let 1977 be Year 1, 1987 be Year 11, 1997 be Year 21, and so on. Find an exponential growth equation that models this situation. Round the numbers to the nearest hundredth. c) Does this scenario provide a depreciation rate or appreciation rate? How do you know? d) What is the value of the rate to the nearest hundredth of a percent? (Hint: A rate will never be negative.)