A business purchases a piece of equipment for $25000. The equipment will be replaced in 10 years at which time its salvage value is expected to be $2000. Write linear equation giving the value V of the equipment during the 10years.
V=slope is 23000/10=-2300
V= -2300t+25000
Well, well, well, let's put our clown shoes on and solve this equation with a sprinkle of humor.
Now, we have a piece of equipment worth $25,000 at the start. As time flies by, let's assume that the value of this equipment is going to depreciate linearly over the course of ten years until it reaches a salvage value of $2,000.
So, my dear friend, we'll use the equation y = mx + b, where y represents the value of the equipment over time, x represents the number of years, m represents the depreciation rate, and b represents the initial value.
In our case, the initial value is $25,000, which we can call b. The salvage value is $2,000, which is our b plus some years multiplied by the depreciation rate. "m" is the depreciation rate per year, so we'll have to figure that out.
Since we're going from $25,000 to $2,000 in a span of 10 years, we know that we've got $23,000 of depreciation. Divide that by 10 years, and you get a yearly depreciation rate of $2,300.
Putting it all together, our linear equation becomes:
V = -2300x + 25000
Don't worry, I promise the math is much simpler than my juggling skills!
To write a linear equation that represents the value of the equipment during the 10-year period, we need two sets of information:
1. The initial value of the equipment.
2. The rate of depreciation.
Given that the equipment was purchased for $25,000 and its salvage value after 10 years is expected to be $2,000, we can calculate the rate of depreciation.
Depreciation = Initial value - Salvage value
Depreciation = $25,000 - $2,000
Depreciation = $23,000
To find the annual depreciation, we divide the total depreciation by the number of years:
Annual Depreciation = Depreciation / Number of years
Annual Depreciation = $23,000 / 10
Annual Depreciation = $2,300
Now that we have the annual depreciation, we can write the linear equation. The equation for the value V of the equipment during the 10 years is:
V = Initial value - (Annual Depreciation * Number of years)
Substituting the given values:
V = $25,000 - ($2,300 * Number of years)
Therefore, the linear equation that represents the value of the equipment during the 10-year period is:
V = $25,000 - ($2,300 * Number of years)
To write a linear equation for the value of the equipment over the course of 10 years, we will use the formula for a line, which is:
y = mx + b
In this case, the value of the equipment (V) will be the y-coordinate, and the number of years (x) will be the x-coordinate. To find the slope (m) and y-intercept (b) for our equation, we need to determine the changing rate of the value of the equipment over time.
We know that the equipment is purchased for $25,000 and its salvage value after 10 years is expected to be $2,000. So, over the span of 10 years, the value of the equipment decreases by $25,000 - $2,000 = $23,000.
To find the changing rate per year (slope), we divide the change in value by the number of years:
m = (change in y) / (change in x)
= ($23,000) / (10 years)
= $2,300 per year
Now that we have the slope, we can find the y-intercept by substituting one of the given points (x, y) into the equation.
Let's use the initial purchase: (0 years, $25,000)
So, x = 0 and y = $25,000.
Substituting these values into the equation, we have:
$25,000 = ($2,300 per year) * 0 + b
$25,000 = b
Therefore, the y-intercept (b) is $25,000.
Now we can write the linear equation for the value (V) of the equipment during the 10 years:
V = $2,300x + $25,000
This equation represents the value of the equipment (V) at any given year (x) during the 10-year period.