Concept explainers
Depreciation A construction company purchases a bulldozer for $ 160,000. Each year the value of the bulldozer depreciates by 20% of its value in the preceding year. Let Vn be the value of the bulldozer in the nth year. (Let n = 1 be the year the bulldozer is purchased.)
- (a) Find a formula for Vn.
- (b) In what year will the value of the bulldozer be less than $100,000?
(a)
To find: The formula for the value of bulldozer in the nth year.
Answer to Problem 71E
The formula for the value of bulldozer in the nth year is
Explanation of Solution
Given:
The purchase value of bulldozer is $160,000. Each year the value of bulldozer decreases by 20% of its preceding year.
Calculation:
The purchase value of bulldozer is $160,000. The value decreased by 20% each year.
The value of bulldozer in the second year is calculated as Purchase value minus the depreciated value.
The value of bulldozer in the third year is,
In general the value of bulldozer denoted by
Thus, the formula for the value of bulldozer in the nth year is
(b)
To find: The year at which the value of bulldozer is less than $100,000.
Answer to Problem 71E
Solution:
The value of bulldozer is less than $100,000 in 4th year.
Explanation of Solution
Given:
The purchase value of bulldozer is $160,000. Each year the value of bulldozer decreases by 20% of its preceding year.
Calculation:
Use the formula from part (a) of the solution to find the value of bulldozer in the 3rd year.
The formula for the value of bulldozer in the nth year is,
Substitute 3 for n in the above formula.
The value of bulldozer is $102400 that is more than $100000.
Again use the formula from part (a) of the solution to find the value of bulldozer in the 4th year.
The formula for the value of bulldozer in the nth year is,
Substitute 4 for n in the above formula.
The value of bulldozer is $81920 that is less than $100000.
Thus, the value of bulldozer is less than $100000 in 4th year.
Chapter 12 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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