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Exponential Depreciation

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Exponential Depreciation

Section 5-6

- 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

- Chevrolet Corvette 2-door Coupe in good condition

- 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

- 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 Depreciation
Y = A

A = starting value of car

r = percent of depreciation

x = time in years

Y = value of the car after x years

- 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

- 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

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

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

- Page 257, 2 - 6

Exponential Depreciation

Section 5-6

- 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

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 =

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 =

- 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

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 =

= 1 - r

= 8.1%

- 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

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 =

= 1 - r

= 10 %

Worksheet