5.5: LINEAR AUTOMOBILE DEPRECIATION OBJECTIVES
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1 Section 5.5: LINEAR AUTOMOBILE DEPRECIATION OBJECTIVES Write, interpret, and graph a straight line depreciation equation. Interpret the graph of a straight line depreciation. Key Terms depreciate appreciate straight line depreciation slope straight line depreciation equation Chapter 5: Automobile Ownership 1
2 Car Prices Over Time: What Happens? 1. Most cars will not be worth their purchase prices as they get older. Most cars depreciate or lose value over time. 2. Some cars, collectibles for example, increase in value over time, or appreciate. How do cars depreciate? What is the difference between the two graphs? graph (a) graph (b) Car Prices Over Time: What Happens? 3. The simplest form of depreciation is straight line depreciation where the car loses the same amount of value each year. What does this amount represent about the line? Recall: SLOPE! By determining the linear model of depreciation, you can calculate the value of the car at any time. Chapter 5: Automobile Ownership 2
3 Straight Line Depreciation We will use the graph at the right to determine the straight line depreciation equation. Recall: Slope-intercept Form of a Linear Equation The car was originally worth $27,500. What does this initial value represent? intercept of the line What can we calculate next? The slope of the line Example 1 The straight line depreciation equation for a car given as 2,850 29,925. (a) How much value does the car lose per year? (b) Determine the value of the car after 5 years. (c) Determine the value of the car after 39 months. (d) How many years will it take for the car to totally depreciate? Chapter 5: Automobile Ownership 3
4 Straight Line Depreciation If you know the initial value of the car and how long the car takes to depreciate, can you write the straight line depreciation equation? Recall: Intercepts of a Linear Equation When (time), the value of the car,, represents the initial value of the car. The intercept is,. When (value of the car), the time,, represents how long the car takes to totally depreciate. The intercept is,. Example 2 Suppose that you purchase a car for $27,000. According to your online research, this make and model of car loses all of its marketable value after 12 years. If this car depreciates in a straight line form, what are the intercepts of the depreciation equation? Chapter 5: Automobile Ownership 4
5 Recall: Calculate the slope of a line passing through two points slope Δ Δ Example 3 Use the intercepts from example 2 to determine the slope of the straight line depreciation model. Recall: Slope-Intercept Form of a Equation Example 4 Write the equation for the straight line depreciation model. Chapter 5: Automobile Ownership 5
6 Example 5 Suppose that you purchased a car five years ago at a price of $27,600. According to your research on this make and model, similar cars have straight line depreciated to zero value after 12 years. How much will your car be worth after 66 months? Expense vs. Depreciation Most drivers finance (or lease) a new car over a period of time rather than pay for the car in full up front. Regardless if financing or leasing a new a car, owners pay for the car on a monthly basis. The money owners pay out of pocket for the car represents an expense. What happens to the car over this same period of time as you pay for the cost of the car? Chapter 5: Automobile Ownership 6
7 Example 6 Rachel bought a new car for $33,600. She made a $4,000 down payment and pays $560 each month for 5 years to pay off her loan. She knows from her research that the make and model of the car she purchased straight line depreciates to zero over 10 years. (a) Write the expense function. (b) Write the straight line depreciation function. Example 6 Continued (c) Using the graphing calculator, graph these functions on the same set of axes. What is your graphing window? (d) Interpret the region before, at and after the intersection point. (e) When will the expense and depreciation amounts be equal? Chapter 5: Automobile Ownership 7
8 Example 7 Joey bought a used car for $9,450. He made a $1,450 down payment and pays $167 each month for 4 years to pay off her loan. He knows that the car he purchased straight line depreciates to zero over 15 years. (a) Write the expense function. (b) Write the straight line depreciation function. (c) When will the expense and depreciation amounts be equal? Chapter 5: Automobile Ownership 8
Objective Today I will calculate the linear depreciation of an automobile. Bellwork 1) What do you think depreciate means?
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