A copier purchased new for 4800 depreciate in value $500 each year the function that models this equation is
The function that models this equation is:
f(x) = 4800 - 500x
where f(x) represents the value of the copier after x years.
To find the function that models the depreciation of the copier, we can use the concept of linear depreciation. Linear depreciation means that the value of the copier decreases by a fixed amount each year.
Let's break down the given information:
- The copier was purchased new for $4800.
- It depreciates in value by $500 each year.
The function that models this equation can be represented as:
V(t) = P - r * t
Where:
- V(t) represents the value of the copier after t years.
- P represents the initial purchase cost of the copier ($4800 in this case).
- r represents the annual depreciation rate ($500 in this case).
- t represents the number of years since the purchase.
Substituting the given values into the equation, we get:
V(t) = 4800 - 500 * t
Therefore, the function that models the depreciation of the copier is V(t) = 4800 - 500 * t.
To find the function that models the depreciation of the copier, we need to start with the initial value of the copier and then subtract the depreciation amount each year.
Let's say the initial value of the copier is $4800.
Since the copier depreciates $500 each year, we can express the depreciation as a linear function with a negative slope.
The general form of a linear function is y = mx + b, where:
- y represents the value of the copier after x years,
- m is the slope of the function (depreciation amount per year),
- x represents the number of years, and
- b is the initial value of the copier.
In this case, the slope (m) will be -500 since the copier depreciates by $500 each year. The initial value (b) is given as $4800.
Therefore, the function that models the depreciation of the copier is:
y = -500x + 4800
Using this function, you can calculate the value of the copier after a specific number of years.