# Exponential Depreciation - PowerPoint PPT Presentation

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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 Depreciation

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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

### Exponential Depreciation

• Chevrolet Corvette 2-door Coupe in good condition

### 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 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 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 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 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 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 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 Depreciation

• Page 257, 2 - 6

## Exponential Depreciation

Section 5-6

### 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 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 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 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 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 =

= 1 - r

= 8.1%

### 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 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 =

= 1 - r

= 10 %

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