the value of an asset, such as a car, computer, or house, depreciates (goes down) over time. when an assets…

the value of an asset, such as a car, computer, or house, depreciates (goes down) over time. when an assets value decreases by a fixed amount each year, the depreciation is called straight - line depreciation. suppose a truck has an initial value of $12,800 and depreciates $640 per year. answer parts a through e.\na. what two variables are involved in this problem? which variable can best be designated as the dependent variable? as the independent variable?\nthe dependent variable is the value of the truck. the independent variable is the number of years of ownership\n\nb. complete the following table.\n| independent variable | 1 | 2 | 3 | 4 | 5 |\n|--|--|--|--|--|--|\n| dependent variable | 12160 | 11520 | 10880 | 10240 | 9600 |\n\nc. state in words the relationship between the independent and dependent variables. choose the correct relationship below.\na. the dependent variable is obtained by adding the product of the amount of depreciation and the independent variable to the initial value of the truck.\nb. the dependent variable is obtained by subtracting the product of the amount of depreciation and the independent variable from the initial value of the truck.\nc. the dependent variable is obtained by subtracting the product of the value of the truck and the independent variable from the amount of depreciation.\nd. the dependent variable is obtained by adding the product of the value of the truck and the independent variable to the amount of depreciation.

the value of an asset, such as a car, computer, or house, depreciates (goes down) over time. when an assets value decreases by a fixed amount each year, the depreciation is called straight - line depreciation. suppose a truck has an initial value of $12,800 and depreciates $640 per year. answer parts a through e.\na. what two variables are involved in this problem? which variable can best be designated as the dependent variable? as the independent variable?\nthe dependent variable is the value of the truck. the independent variable is the number of years of ownership\n\nb. complete the following table.\n| independent variable | 1 | 2 | 3 | 4 | 5 |\n|--|--|--|--|--|--|\n| dependent variable | 12160 | 11520 | 10880 | 10240 | 9600 |\n\nc. state in words the relationship between the independent and dependent variables. choose the correct relationship below.\na. the dependent variable is obtained by adding the product of the amount of depreciation and the independent variable to the initial value of the truck.\nb. the dependent variable is obtained by subtracting the product of the amount of depreciation and the independent variable from the initial value of the truck.\nc. the dependent variable is obtained by subtracting the product of the value of the truck and the independent variable from the amount of depreciation.\nd. the dependent variable is obtained by adding the product of the value of the truck and the independent variable to the amount of depreciation.

Answer

Explanation:

Step1: Identify the depreciation - based formula

The initial value of the truck is $V_0 = 12800$ and the annual depreciation is $d = 640$. The formula for the value of the truck $V$ (dependent variable) after $t$ (independent variable) years is $V=V_0 - dt$.

Step2: Analyze option A

Option A says $V = V_0+dt$. But since the value of the truck is decreasing (depreciating), this is incorrect.

Step3: Analyze option B

The formula $V = V_0 - dt$ means the dependent variable (value of the truck) is obtained by subtracting the product of the amount of depreciation ($d = 640$) and the independent variable (number of years $t$) from the initial value of the truck ($V_0=12800$). This is correct.

Step4: Analyze option C

The formula described in option C, $d - V\times t$, does not represent the value - depreciation relationship correctly.

Step5: Analyze option D

The formula in option D, $d+V\times t$, also does not represent the value - depreciation relationship correctly.

Answer:

B. The dependent variable is obtained by subtracting the product of the amount of depreciation and the independent variable from the initial value of the truck.