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Understanding Exponential Depreciation Equations: Analysis & Interpretation

Learn to write, interpret, and graph exponential depreciation equations to find depreciation rates, original prices, and depreciated values. Analyze dollar value historical data using exponential decay models. Key terms: exponential depreciation, historical data, depreciation percentage, depreciation rate calculation. Examples cover scenarios such as determining depreciation rates, calculating car values over time, and estimating the original price of depreciated items.

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Understanding Exponential Depreciation Equations: Analysis & Interpretation

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  1. 5-6HISTORICAL AND EXPONENTIAL DEPRECIATION OBJECTIVES Write, interpret, and graphan exponential depreciation equation. Manipulatethe exponential depreciation equation in order to determine time, original price, and depreciated value.

  2. dollar value historical data historical depreciation exponential decay exponential depreciation y = A(1 – r)x Key Terms

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

  4. 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?

  5. 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.

  6. 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?

  7. CHECK YOUR UNDERSTANDING Describe the situation after 4 years.

  8. EXAMPLE 5 A car exponentially depreciates at a rate of 5% per year. If the car is worth $30,000 after 9 months, what was the original price of the car?

  9. 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?

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