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
B
No, the correct answer is D) f(x) = 400x - 3600.
The slope (-400) represents the amount the value decreases each year, and since it is negative, the function needs to subtract that value each year. The y-intercept (3600) represents the initial value of the machine, so it should be added to the slope. Therefore, the equation of the linear function is:
f(x) = -400x + 3600
By simplifying this equation, we get:
f(x) = 400x - 3600
Well, let's think about this situation. We know that the office machine loses $400 each year. If we start with $3600, and subtract $400 each year, we can model that with the equation f(x) = -400x + 3600.
So the correct answer is C) f(x) = -400x + 3600. It looks like our office machine is not appreciating in value! Better put a "Do Not Touch" sign on it to protect its feelings.
To solve this problem, we need to find a linear function that models the given situation.
We are told that the office machine loses $400 each year. This means that the value of the machine decreases by $400 after each year.
Let's break down the given information:
- After 1 year, the machine loses $400, so the value is $3600 - $400 = $3200.
- After 2 years, the machine loses another $400, so the value is $3200 - $400 = $2800.
- After 3 years, the machine loses another $400, so the value is $2800 - $400 = $2400.
Looking at these values, we can see a pattern: the value of the machine decreases by $400 with each passing year. So, for every year x, the machine loses $400x.
Now, let's look at the options:
A) f(x) = 400x + 3600
B) f(x) = -400x - 3600
C) f(x) = -400x + 3600
D) f(x) = 400x - 3600
Since the value of the machine is decreasing each year, the function should have a negative coefficient for x.
Out of the given options, the correct answer is C) f(x) = -400x + 3600, as it has the negative coefficient (-400x) and correctly models the situation where the machine loses $400 each year.
you have the slope (-400) and the y-intercept (3600)
so, what do you think?