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Quant Reasoning chapter 4 EX 2 My Lab Pearson
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Problem solving for chapter four question two
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Calculating Machine Scrap Value: A Step-by-StepGuide
Problem Statement
The scrap value of a machine at the end of its useful life is given by S ( n )=C ¿ , where C is the
original cost, n is the useful life of the machine in years, and r is the constant annual
percentage of value lost. Find the scrap value of the following machine.
Original cost, $53,000; life, 11 years; annual rate of value lost, 9%
Where:
- S(n) is the scrap value
- C is the original cost
- r is the constant annual percentage of value lost
- n is the useful life of the machine in years
Given Information
- Original cost (C): $53,000
- Useful life (n): 11 years
- Annual rate of value lost (r): 9% (0.09 in decimal form)
Step-by-Step Solution
1. Identify the formula:
S ( n )=C ¿
2. Substitute the known values:
S(11) = 53,000(1 - 0.09 ¿11
3. Simplify the expression inside the parentheses:
S(11) = 53,000(0.91 ¿11
4. Use a calculator to compute the result:
S(11) ≈ 18,781.54
5. Round to the nearest cent (if required):
S(11) = $18,781.54
Conclusion
The scrap value of the machine after 11 years is $18,781.54.
Tips
- Round the final answer as specified in the problem (in this case, to the nearest cent).
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