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Use the following to help calculate depreciation:
- depreciation formula:
y = abx
a = original cost of item
b = decay factorRemember to change the percent to decimal and subtract from 1.
x = number of years
y = value of item after given number of years
- calculator
- pencil
- paper
Example 1
James bought a new car at a cost $20,000. The car depreciates approximately 15% of its value each year.
- decay factor: 1 - 0.15 = 0.85 (remember the decay factor is 0 < b < 1)
- y = abx = 20,000(0.85)x
- How much will his car be worth in 5 years?
- y = 20,000(0.85)5 = $8,874.11
Let's take a look at another problem.
Example 2
A computer valued at $3500 depreciates at the rate of 13.3% per year. Let's start by identifying our variables.
a =
b =
Answer:
a = 3500
b = 0.867
Write a function that models the value of the computer.
y = ( )x
Answer: y = 3500(0.867)x
What is the value of the computer after 2 years?
y = 3500(0.867)2 = $
Answer: $2,630.91
Example 3
Suppose you are interested in purchasing a used car that costs $11,500. The expected depreciation of the car is 20% per year. What is the estimated depreciated value of the car after 4 years?
a =
b =
x =
Answer:
a = 11,500
b = 0.80
x = 4
Write a function that models the value of the computer.
y = ( )^
Answer: y = 11,500(0.80)4
What is the value of the computer after 2 years?
y = 11,500(0.80)4= $
Answer: $4,710.40
Example 4
The value of a computer has a decay factor of 0.70 per year. After 3 years, the computer is worth $2058. What was the original value of the computer.
y = abx
= a(0.70)3
Answer: 2058 = a(0.70)3
2058 = a( )
Answer: 2058 = a(0.343)
a =
Answer: a = $6,000
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