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Chapter 8: Problem 1

The value of almost everything you own, such as a car, computer, or appliance, depreciates over time. When the value decreases by a fixed amount each year, the depreciation is called straightline depreciation. Suppose your car has an initial value of \(\$ 16,750\) and depreciates \(\$ 1030\) per year. a. State a question that you might want answered in this situation. b. What two variables are involved in this problem? c. Which variable do you think should be designated as the input variable? d. Complete the following table. e. State in words the relationship between the value of the car and the number of years the car is owned. f. Use appropriate letters to represent the variables involved and translate the written statement in part e to an equation. g. If you plan to keep the car for 7 years, determine the value of the car at the end of this period. Explain the process you used.

Short Answer

Expert verified
Answer: The car will be worth $9,540 after 7 years.

Step by step solution

01

(a. State a question related to this situation)

(Given the initial value of the car and the annual depreciation amount, how much will the car be worth after a certain number of years?)
02

(b. Identify the two variables involved)

(The two variables involved in this problem are: the value of the car (V) and the number of years the car is owned (t).)
03

(c. Determine the input variable)

(The input variable is the number of years the car is owned (t), as it affects the value of the car.)
04

(d. Complete the table)

(In order to complete the table, we will create a formula for the value of the car after a certain number of years and then apply this formula for various given years.)
05

(Formula for the value of the car)

(The formula for the value of the car after t years is given by: V = 16750 - 1030 * t, where V is the value of the car and t is the number of years.)
06

(Completing the table)

(Use the formula to evaluate the value of the car for different years.) | Years owned (t) | Value of the car (V) | |-----------------|--------------------------| | 0 | \(16750 - 1030 * 0 = 16750\)| | 1 | \(16750 - 1030 * 1 = 15720\)| | 2 | \(16750 - 1030 * 2 = 14690\)| | 3 | \(16750 - 1030 * 3 = 13660\)| and so on...
07

(e. State the relationship between the value of the car and the number of years)

(The value of the car decreases by a fixed amount of $1030 per year, as it depreciates over the years.)
08

(f. Translating the written statement to an equation)

(Using V for the value of the car and t for the number of years, we can represent the relationship as: V = 16750 - 1030 * t)
09

(g. Determine the value of the car after 7 years)

(Using the equation, we can determine the value of the car after 7 years of ownership: V = 16750 - (1030 * 7) = 16750 - 7210 = 9540. The car will be worth $9540 after 7 years.)

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