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Ch 5 Automobile ownership

Ch 5 Automobile ownership. 5.6 Historical and Exponential Depreciation. How does a car lose its value??. What does devaluation mean? What does it mean for a car? What factors might contribute to a car loosing its value?. Last section.

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Ch 5 Automobile ownership

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  1. Ch 5 Automobile ownership 5.6 Historical and Exponential Depreciation

  2. How does a car lose its value?? • What does devaluation mean? • What does it mean for a car? • What factors might contribute to a car loosing its value?

  3. Last section.. • Last section we talked about a car losing a particular dollar value (value of money that something is worth) each year • A car doesn’t always lose same amount every year • You can get an idea as to how much a car can lose by looking at historical data, prices from the past that a car was worth • This is called historical depreciation, the devaluation of a car using historical data

  4. Prices of a chevrolet 2 door coupe • Scatterplot of the data • Table of the data

  5. Exponential decay • The scatterplot on the previous slide represents exponential decay • Rather than the value decreasing by the same amount each year, it decreases by the same percentage each year • When speaking in terms of the devaluation of automobiles, we call this exponential depreciation • General formula

  6. Example 1 • Determine an exponential depreciation equation that models the data in the table.

  7. Check your understanding • How might a better-fitting exponential depreciation equation look when superimposed over the same scatterplot?

  8. Example 2 • What is the depreciation percentage for the 10 years of car prices as modeled by the exponential depreciation equation found in Example 1?

  9. Check your understanding • After entering a set of automobile value data into a graphing calculator, the following exponential regression equation information is given: y = a*b^x, a = 32,567.98722, b = 0.875378566. Round the values to the nearest hundredth. Determine the depreciation percentage.

  10. Example 3 • Eamon purchased a four-year-old car for $16,400. When the car was new, it sold for $23,000. Find the depreciation rate to the nearest tenth of a percent.

  11. Example 4 • A car originally sold for $26,600. It depreciates exponentially at a rate of 5.5% per year. When purchasing the car, Richard put $6,000 down and pays $400 per month to pay off the balance. After how many years will his car value equal the amount he paid to date for the car?

  12. Example 5 • A car exponentially depreciates at a rate of 6% per year. Beth purchased a 5-year-old car for $18,000. What was the original price of the car when it was new?

  13. Example 6 • Leah and Josh bought a used car valued at $20,000. When this car was new, it sold for $24,000. If the car depreciates exponentially at a rate of 8% per year, approximately how old is the car?

  14. Ch 5 Asnt 6 • Pg. 257 #2, 4, 7, 9, 11, 14, 18

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