Exponential Depreciation
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Transcript of Exponential Depreciation
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Exponential Depreciation
Section 5-6
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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 Chevrolet Corvette 2-door Coupe in
good conditionAge Value
($)Age Value
($)1 24,230 6 15,2452 22,355 7 14,0753 20,645 8 13,1004 18,070 9 12,3255 16,256 10 11,525
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Exponential Depreciation
0 2 4 6 8 10 1210,00012,00014,00016,00018,00020,00022,00024,00026,000
Y-Values
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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
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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
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Exponential Depreciation Exponential Depreciation
Y = A
A = starting value of carr = percent of depreciationx = time in yearsY = value of the car after x years
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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
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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
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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
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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
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Exponential Depreciation Page 257, 2 - 6
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Exponential Depreciation
Section 5-6
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Exponential Depreciation Exponential Depreciation
Y = A
A = starting value of carr = percent of depreciationx = time in yearsY = value of the car after x years
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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 =
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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 =
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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
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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
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Exponential Depreciation𝟏𝟔 ,𝟒𝟎𝟎𝟐𝟑 ,𝟎𝟎𝟎=(𝟏−𝒓 )𝟒()
14()
14
= 1 - r
𝑟=1−(16,40023,000
)14 = 8.1%
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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
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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
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Exponential Depreciation𝟏𝟒 ,𝟐𝟎𝟎𝟐𝟒 ,𝟎𝟎𝟎 =(𝟏−𝒓 )𝟓()
15()
15
= 1 - r
𝑟=1−(14,20024,000
)15= 10 %
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Exponential DepreciationWorksheet
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Exponential Depreciation
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Exponential Depreciation
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Exponential Depreciation