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:

Stock Price

The cost of purchasing a single share of a company, fluctuating based on supply and demand in the market.

Strike Price

The set price at which an option's owner has the right to purchase (for a call option) or sell (for a put option) the underlying asset.

Stock Call Option

A financial derivative that gives the buyer the right, but not the obligation, to buy a specific stock at a predetermined price within a set period.

Stock Price

The current price at which a share of a company is bought or sold in the stock market, reflecting the company's perceived value and investor demand.