An office machine purchased new for $3600
loses $400 each year.
Assume the value continues to decrease the same amount each year. If f(x) represents the value of the office machine after x years, which linear function models the given situation?
A. f(x) = 400x + 3600
B. f(x) = -400x - 3600
C. f(x) = -400x + 3600
D. f(x) = 400x - 3600
The office machine loses $400 each year, so the value will decrease by $400 for each year that passes. The initial value is $3600, so the linear function that models the situation is:
f(x) = -400x + 3600
The correct answer is C. f(x) = -400x + 3600.
An office machine purchased new for $3600
loses $400 each year.
How many years will it take for the office machine's value to equal zero?
A. 5
B. 6
C. 9
D. 12
The office machine loses $400 each year, so we need to determine the number of years it will take for the value to reach zero. To find the number of years, we can set up the equation:
-400x + 3600 = 0
Solving for x:
-400x = -3600
x = 9
Therefore, it will take 9 years for the office machine's value to equal zero.
The correct answer is C. 9 years.
The correct linear function that models the situation is C. f(x) = -400x + 3600.
According to the given information, the office machine loses $400 each year. This means that the value of the office machine is decreasing by $400 every year.
To model this situation using a linear function, we need to write an equation of the form f(x) = mx + b. Here, x represents the number of years and f(x) represents the value of the office machine after x years.
Since the office machine loses $400 each year, the slope, m, of the linear function is -400. The negative sign indicates a decrease in value.
The initial value of the office machine, when it was purchased new, is $3600. This gives us the y-intercept, which is represented by the constant term, b, in the linear function.
Therefore, the linear function that models the given situation is:
f(x) = -400x + 3600.
Hence, option C, f(x) = -400x + 3600, is the correct answer.
To find the linear function that models the given situation, we need to analyze how the value of the office machine decreases over time. According to the information provided, the machine loses $400 each year.
Let's break down the problem step-by-step to understand the correct equation:
1. Start with the initial value of the machine: $3600.
2. Each year, the value decreases by $400.
3. Since the value decreases, we need a negative term in the equation.
4. The equation should be in the form f(x) = mx + b, where m represents the rate of change (slope) and b represents the initial value (y-intercept).
Now we can determine the correct linear function:
- The rate of change (slope): The machine loses $400 each year, so the slope is -400.
- The initial value (y-intercept): The machine starts with a value of $3600, so the y-intercept is 3600.
Plugging in these values, we get:
f(x) = -400x + 3600
Therefore, the correct linear function that models the given situation is option C:
f(x) = -400x + 3600.