An office machine purchased new for $3600
loses $400 each year.
1× Assume the value continues to declease 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 answer is C. f(x) = -400x + 3600.
Since the office machine loses $400 each year, we can represent the decrease in value as a negative value.
The function f(x) represents the value of the office machine after x years, so it should be the starting value ($3600) minus the decrease in value (-$400x).
Therefore, the linear function that models the given situation is f(x) = -400x + 3600.
The correct linear function that models the given situation is option B: f(x) = -400x - 3600.
This is because the machine loses $400 each year, which indicates a constant decrease. The negative sign in front of 400 represents the decrease, and the -3600 represents the initial value of the machine ($3600) being subtracted since it loses value every year.
To determine the linear function that models the given situation, we need to understand the pattern in which the value decreases each year.
Since the office machine loses $400 each year, we know that the decrease is constant. This means that for every additional year, the value decreases by the same amount.
Let's break down the information given:
- The starting value of the office machine is $3600.
- For each year, the value decreases by $400.
Using this information, we can set up an equation to represent the situation.
The equation should take the form: f(x) = mx + b, where f(x) represents the value of the office machine after x years, m is the slope (rate of change), and b is the initial value.
In this case, since the value decreases by $400 each year, the slope (m) is -400. The initial value (b) is $3600.
Thus, the linear function that models the given situation can be written as:
f(x) = -400x + 3600
Therefore, the correct answer is C. f(x) = -400x + 3600.