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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
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