To model the given situation, we need a linear function that represents the decrease in value of the office machine. Since the office machine loses $400 each year, the function must include a negative coefficient for the years.
Looking at the options:
A. f(x) = 400x + 3600 - This option has a positive coefficient for the years, which means the value of the office machine would increase over time, not decrease.
B. f(x) = −400x − 3600 - This option has a negative coefficient for the years, which represents the decrease in value. So this could be a possible linear function.
C. f(x) = −400x + 3600 - This option has a positive coefficient for the years, which means the value of the office machine would increase over time, not decrease.
D. f(x) = 400x − 3600 - This option has a positive coefficient for the years, which means the value of the office machine would increase over time, not decrease.
So, the linear function that models the given situation is:
B. f(x) = −400x − 3600.
To find out how many years it will take for the office machine's value to equal zero, we can set the linear function to zero and solve for x:
−400x − 3600 = 0
Adding 3600 to both sides:
−400x = 3600
Dividing both sides by -400:
x = -9
Since the number of years cannot be negative in this context, we discard the negative solution.
Therefore, it will take 9 years for the office machine's value to equal zero.
So the correct option is not listed among the given responses.
Modeling with Linear Functions
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 + 3600f(x) = 400x + 3600
B. f(x) = −400x − 3600f(x) = −400x − 3600
C. f(x) = −400x + 3600f(x) = −400x + 3600
D. f(x) = 400x − 3600
How many years will it take for the office machine's value to equal zero?
Responses
A. 55
B. 66
C. 99
D. 12
1 answer