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Exponential Depreciation. Section 5-6. Exponential Depreciation. In the previous section, we learned about straight line depreciation Cars lose the same value each year If this is not the case, how could we determine the value of a car after a certain number of years Look at historical data.

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Exponential depreciation1
Exponential Depreciation

  • In the previous section, we learned about straight line depreciation

    • Cars lose the same value each year

  • If this is not the case, how could we determine the value of a car after a certain number of years

    • Look at historical data


Exponential depreciation2
Exponential Depreciation

  • Chevrolet Corvette 2-door Coupe in good condition



Exponential depreciation4
Exponential Depreciation

  • The actual graph of this depreciation appears to be curved

    • It is not a straight line

  • The car value seems to drop more at the beginning of the car’s lifetime and less as each year passes


Exponential depreciation5
Exponential Depreciation

  • This is known as exponential decay

    • The value of the car decreases by the same percentage each year

    • Model is known as Exponential Depreciation


Exponential depreciation6
Exponential Depreciation

  • Exponential Depreciation

    Y = A

    A = starting value of car

    r = percent of depreciation

    x = time in years

    Y = value of the car after x years


Exponential depreciation7
Exponential Depreciation

  • You buy a car that originally sells for $25,000. It exponentially depreciates at a rate of 4 ¼ % per year.

  • Write an exponential depreciation equation for this car.

    Y = 25,000


Exponential depreciation8
Exponential Depreciation

  • Tanya’s new car sold for $23,856. Her online research indicates that the car will depreciate exponentially at a rate of 6 % per year.

  • Write an exponential depreciation equation for this car.

    Y = 23,856


Exponential depreciation9
Exponential Depreciation

You buy a used car for $12,500. The car depreciates exponentially at a rate of 5 ¼% per year. How much will the car be worth after 5 years?

Y = 12,500

Y = 12,500

Y = $9,545.66


Exponential depreciation10
Exponential Depreciation

Sharon purchased a used car for $24,600. The car depreciates exponentially by 8% per year. How much will the car be worth after 5 years?

Y = 24,600

Y = 24,600

Y = $16,213.41


Exponential depreciation11
Exponential Depreciation

  • Page 257, 2 - 6



Exponential depreciation13
Exponential Depreciation

  • Exponential Depreciation

    Y = A

    A = starting value of car

    r = percent of depreciation

    x = time in years

    Y = value of the car after x years


Exponential depreciation14
Exponential Depreciation

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?

Y =

18,000 =

18,000 = A

A =

A =


Exponential depreciation15
Exponential Depreciation

A car exponentially depreciates at a rate of 9% per year. Beth purchased a 7-year old car for $14,500. What was the original price of the car when it was new?

Y =

14,500 =

14,500 = A

A =

A =


Exponential depreciation16
Exponential Depreciation

  • Yesterday, we:

  • Found the equation for exponential depreciation

  • Calculated the value of a car after “x” number of years

  • Today, we are going to find the rate of depreciation of a car


Exponential depreciation17
Exponential Depreciation

You buy a 4-year old car for $16,400. When the car was new, it sold for $23,000. Find the depreciation rate.

Y =

16,400 =


Exponential depreciation18
Exponential Depreciation

= 1 - r

= 8.1%


Exponential depreciation19
Exponential Depreciation

  • Steps to finding rate

  • Substitute variables into the equation

  • Divide both sides by starting price (A)

  • Raise both sides to the reciprocal of x

  • Re-write equation with r isolated

  • Plug into calculator

  • Convert to a percent


Exponential depreciation20
Exponential Depreciation

Brad purchased a 5-year old car for $14,200. When the car was new, it sold for $24,000. Find the depreciation rate.

Y =

14,200 =


Exponential depreciation21
Exponential Depreciation

= 1 - r

= 10 %






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