An office machine purchased new for $3600 loses $400 each year.

Question

Question 1
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?
Responses
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 − 3600f(x) = 400x − 3600
Question 2
How many years will it take for the office machine's value to equal zero?
Responses
A 55
B 66
C 99
D 12

Answer 1

Question 1:
The correct linear function that models the given situation is:

C f(x) = −400x + 3600

Question 2:
To find out how many years it will take for the office machine's value to equal zero, we set the function f(x) equal to zero and solve for x:

−400x + 3600 = 0

Simplifying:

−400x = −3600

Dividing by −400:

x = 9

Therefore, it will take 9 years for the office machine's value to equal zero.