A school district purchases a high-volume printer, copier, and scanner for $21,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2,500. Write a linear equation giving the value of the equipment during the 10 years it will be in
Use)
A) $V = - 1850 + 21,000 t$
B) $V = - 1850 t - 21,000$
C) $V = 1850 t - 21,000$
D) $V = - 1850 t + 21,000$
E) $V = 1850 t + 21,000$

Question

A school district purchases a high-volume printer, copier, and scanner for $21,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2,500. Write a linear equation giving the value of the equipment during the 10 years it will be in
Use) 
A) $V = - 1850 + 21,000 t$
B) $V = - 1850 t - 21,000$
C) $V = 1850 t - 21,000$
D) $V = - 1850 t + 21,000$
E) $V = 1850 t + 21,000$

Quizplus · Accepted Answer

Since the value of the equipment is decreasing over time, the coefficient of the t-term should be negative. Furthermore, at t=0 (the time of purchase), the value is $21,000 which is the y-intercept. Therefore, the equation should be in the form V = mt + b, where b = 21,000. The value at the end of 10 years is $2,500 which means that the equipment loses $18,500 of value over 10 years. This gives a slope of -1850. Hence, the equation is V = -1850t + 21,000 which is choice D.

A School District Purchases a High-Volume Printer, Copier, and Scanner V=−1850+21,000tV = - 1850 + 21,000 tV=−1850+21,000t

A School District Purchases a High-Volume Printer, Copier, and Scanner $V = - 1850 + 21,000 t$