And Office machine purchased new for $3600 loses $400 each year assuming the value continues to decrease the same amount each year if F X represents the value of the Office machine after eight years which linear function models that given situation
To find the linear function that models the given situation, we can use the slope-intercept form of a linear equation, which is given by:
y = mx + b
Where:
y represents the value of the office machine after a certain number of years (in this case, 8 years).
x represents the number of years.
m represents the slope (rate of decrease per year).
b represents the initial value of the office machine.
In this case, we know that the machine loses $400 each year, so the slope (m) is -400. Since the machine starts at $3600, the initial value (b) is 3600.
Now, we can substitute the values into the equation:
y = -400x + 3600
So, the linear function that models the given situation is: F(x) = -400x + 3600.
To find the linear function that models the given situation, we need to determine the equation of the line that represents the value of the office machine over time.
Let's assign "t" as the number of years and "V" as the value of the office machine. We know that the office machine is purchased new for $3600 and loses $400 each year.
After one year: V = $3600 - $400 = $3200
After two years: V = $3200 - $400 = $2800
After three years: V = $2800 - $400 = $2400
And so on, until after eight years: V = $3600 - ($400 * 8) = $3600 - $3200 = $400.
We can observe that the value of the office machine decreases by $400 each year. Therefore, the slope of the linear function representing the value over time is -400.
The initial value of the office machine is $3600, so the y-intercept (where the line crosses the y-axis) is $3600.
Using the slope-intercept form of a linear equation (y = mx + b), where m is the slope and b is the y-intercept, we can write the equation as:
V = -400t + 3600
Finally, substituting "F" for "V" and "X" for "t," the equation becomes:
F = -400X + 3600
Therefore, the linear function that models the given situation is F = -400X + 3600.
To find the linear function that models the given situation, we need to determine the rate at which the value of the office machine decreases each year.
We know that the office machine loses $400 each year. So, after one year, the value will be $3600 - $400 = $3200. After two years, the value will be $3200 - $400 = $2800, and so on.
We can observe that the value decreases by $400 each year, which means the slope of the linear function is -400 (since it is decreasing).
Now let's find the y-intercept. The initial value of the office machine is $3600, so when x = 0 (representing the initial year), the value of the machine should be $3600.
Putting all this together, the linear function that models the given situation can be expressed as follows:
F(x) = -400x + 3600
Where:
- F(x) represents the value of the office machine after x years.
- -400 is the slope, representing the $400 decrease each year.
- x is the number of years.
- 3600 is the initial value of the office machine.
So, for example, to find the value of the office machine after eight years, we substitute x = 8 into the function:
F(8) = -400(8) + 3600
F(8) = -3200 + 3600
F(8) = $400
Therefore, the value of the office machine after eight years would be $400.