Solve the Problem $a _ { n } = 100,000 ( 0.83 ) ^ { n - 1 }$

question 55

Multiple Choice

Solve the problem.
-A farmer depreciates a $100,000 tractor. He estimates that the resale value of the tractor n years after purchase is 83% of its value from the previous year.
a. Write a formula for the nth term of a sequence that represents the resale value of the tractor n years After purchase.
b. What will the resale value be after 7 years? Round to the nearest $1000.

• A) a. \(a _ { n } = 100,000 ( 0.83 ) ^ { n - 1 }\)
• b. \(\$ 27,000\)
• B) a. \(a _ { n } = 100,000 ( 0.83 ) ^ { n - 1 }\)
• b. \(\$ 33,000\)
• C) a. \(a _ { n } = 100,000 ( 0.83 ) ^ { n }\)
• b. \(\$ 27,000\)
• D) a. \(a _ { n } = 100,000 ( 83 ) ^ { n }\)
• b. \(\$ 33,000\)

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Definitions:

Favorable

A term used in accounting and finance to indicate that actual costs were lower than planned or budgeted costs.

Standard Cost System

An accounting system that uses standard costs for products or services for the purpose of controlling costs and assessing operational performance.

Standard Direct Labor-Hours

The estimated amount of labor hours required to produce a unit of product, used in budgeting and variance analysis.

Denominator Level

The activity level used to compute a predetermined overhead rate, often reflecting capacity or expected usage.