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

Age Value ($)

Age Value ($)

1 24,230 6 15,245

2 22,355 7 14,075

3 20,645 8 13,100

4 18,070 9 12,325

5 16,256 10 11,525

Exponential Depreciation

0 2 4 6 8 10 1210,00012,00014,00016,00018,00020,00022,00024,00026,000

Y-Values

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 carr = percent of depreciationx = time in yearsY = 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 DepreciationYou 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 = 12,500Y = 12,500Y = $9,545.66

Exponential DepreciationSharon 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 = 24,600Y = 24,600Y = $16,213.41

Exponential Depreciation Page 257, 2 - 6

Exponential Depreciation

Section 5-6

Exponential Depreciation Exponential Depreciation

Y = A

A = starting value of carr = percent of depreciationx = time in yearsY = value of the car after x years

Exponential DepreciationA 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 DepreciationA 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:1) Found the equation for exponential

depreciation2) 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 DepreciationYou 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 =

𝟏𝟔 ,𝟒𝟎𝟎𝟐𝟑 ,𝟎𝟎𝟎

=(𝟏−𝒓 )𝟒

Exponential Depreciation

𝟏𝟔 ,𝟒𝟎𝟎𝟐𝟑 ,𝟎𝟎𝟎

=(𝟏−𝒓 )𝟒()14()

14

= 1 - r

𝑟=1−( 16,40023,000

)14 = 8.1%

Exponential Depreciation Steps to finding rate1) Substitute variables into the

equation2) Divide both sides by starting price

(A)3) Raise both sides to the reciprocal of

x4) Re-write equation with r isolated5) Plug into calculator6) Convert to a percent

Exponential DepreciationBrad 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 = 𝟏𝟒 ,𝟐𝟎𝟎𝟐𝟒 ,𝟎𝟎𝟎

=(𝟏−𝒓 )𝟓

Exponential Depreciation

𝟏𝟒 ,𝟐𝟎𝟎𝟐𝟒 ,𝟎𝟎𝟎

=(𝟏−𝒓 )𝟓()15()

15

= 1 - r

𝑟=1−( 14,20024,000

)15= 10 %

Exponential DepreciationWorksheet

Exponential Depreciation

Exponential Depreciation

Exponential Depreciation