The value of almost everything you own, such as a car, computer, or appliance, depreciates over time. When the value decreases by a fied amount each year, the depreciation is called straight-line 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.
Year Car is Owned 1 2 3 4 5
Value of Car(s)
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.
b. Variables are the value and the years owned.
c. The number of years owned is Input variable.
d. V = 16,750 - 1030*1 = $15,720.
V = 16,750 - 1030*2 = $14,690.
Finish the table.
e. The value of the car decreases as the years increase.
f. V = 16750 - 1030x.
V = Value of car.
x = The number of years owned.
g. V = 16750 - 1030*7 =]
a. One possible question that could be asked in this situation is: "How does the value of the car change over the years?"
b. The two variables involved in this problem are the number of years the car is owned and the value of the car.
c. In this case, the variable "number of years the car is owned" should be designated as the input variable because it is the independent variable that determines the value of the car.
d. Based on the given information, we can complete the following table:
Year Car is Owned 1 2 3 4 5
Value of Car(s) $16,750 - $1,030 $16,750 - (2 * $1,030) $16,750 - (3 * $1,030) $16,750 - (4 * $1,030) $16,750 - (5 * $1,030)
Using the formula for straight-line depreciation, we subtract $1,030 multiplied by the number of years from the initial value of $16,750 to get the value of the car for each year.
e. The relationship between the value of the car and the number of years the car is owned is that the value decreases by $1,030 each year.
f. Let "V" represent the value of the car and "n" represent the number of years the car is owned. The equation representing the relationship between the value of the car and the number of years can be expressed as:
V = $16,750 - ($1,030 * n)
g. If you plan to keep the car for 7 years, you can plug in "n = 7" into the equation:
V = $16,750 - ($1,030 * 7)
V = $16,750 - $7,210
V = $9,540
The value of the car at the end of 7 years would be $9,540. We used the equation from part f and substituted "n = 7" to find the value.