Objective Today I will calculate the linear depreciation of an automobile. Bellwork 1) What do you think depreciate means?

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1 Objective Today I will calculate the linear depreciation of an automobile. Bellwork 1) What do you think depreciate means? lose value 2) In the equation y = 200x + 450, explain what 200 and 450 mean. 200 = slope, 450 = y intercept (starting value) 3) What type of auto insurance covers damage to your vehicle not caused by an accident? What about damage done to someone else's property? comprehensive/property damage 4) Calculate the mean, median, mode, and IQR of the following data set: $250, $250, $300, $350, $450, $500, $800 mean: $ median: $350 mode: $250 IQR: $250

2 Depreciate: When a car loses value over time.

3 Straight Line Depreciation: When a car loses the same value each year until it is worthless.

4 Slope: In the equation y = mx + b, m is the slope. It is the amount that the car will depreciate per year.

5 y intercept: In the equation y = mx + b, b is the y intercept. It is the initial value of the vehicle.

6 Time in Years: In the equation y = mx + b, x is the car s age in years.

7 Value of the Car: In the equation y = mx + b, y is the value of the car after the given time frame.

8 Another Equation that You Will Need. Once you know the slope (rate of change) for the problem, plug the slope and one of the point vales into the point slope form.

9 Example #1 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. That is, it depreciates to a value of zero dollars 12 years after the purchase date. If this car depreciates in a straight line form, what are the intercepts of the depreciation equation?

10 Example #2 A car sells for $38,500 and totally depreciates after 9 years. If this car straight line depreciates, what are the intercepts of the straight line depreciation equation?

11 Example #3 Determine the slope of the straight line depreciation equation for the situation in Example 1.

12 Example #4 Determine the slope of the straight line depreciation equation for the situation in Example 2.

13 Example #5 Write the straight line depreciation equation for the situation discussed in Example 1.

14 Example #6 Write the straight line depreciation equation for the situation discussed in Example 2.

15 Example #7 Sketch the graph of the equation from Example #5.

16 Example #8 Sketch the graph of the equation from Example #6.

17 Example #9 Write and graph the straight line depreciation equation for a car that was purchased for $22,000 and totally depreciates after 11 years.

18 Example #10 Write and graph the straight line depreciation equation for a car that was purchased for $37,900 and totally depreciates after 10 years.

19 Example #11 Suppose that Jack purchased a car five years ago at a price of $27,600. According to research on this make and model, similar cars have straight line depreciated to zero value after 12 years. How much will this car be worth after 66 months?

20 Example #12 The straight line depreciation equation for a car is y = 4,000x + 32,000. In approximately how many years will the car s value decrease by 25%?

21 Celine 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. Create an expense and depreciation function. b. Graph these functions on the same axes. c. Interpret the region before, at, and after the intersection point.

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