Solve the problem.
-A piece of equipment was purchased by a company for $10,000 and is assumed to have a salvage value of $3,000 in 10 years. If its value is depreciated linearly from $10,000 to $3,000, find a linear equation in the form V
= mt + b, t time in years, that will give the salvage value at any time e t,
A) V = 700t + 10,000
B) T = - 700V + 10,000
C) V = - 700t - 10,000
D) V = - 700t + 10,000

Question

Solve the problem.
-A piece of equipment was purchased by a company for $10,000 and is assumed to have a salvage value of $3,000 in 10 years. If its value is depreciated linearly from $10,000 to $3,000, find a linear equation in the form V
= mt + b, t time in years, that will give the salvage value at any time e t, 
A) V = 700t + 10,000 
B) T = - 700V + 10,000 
C) V = - 700t - 10,000 
D) V = - 700t + 10,000

Quizplus · Accepted Answer

To find the linear equation in the form V = mt + b, we need to use the two given data points: (0, $10,000) and (10, $3,000) - where time t is in years and value V is in dollars.

Using the point-slope form for a linear equation, we get:

V - 10000 = (3000 - 10000)/(10 - 0) * t

Simplifying, we get:

V = -700t + 10000

Therefore, the correct answer is D - V = -700t + 10,000. Using the two points (0,10000) and (10,3000), we can find the slope, m, and y-intercept, b, of the linear equation for V.

Slope, m:
m = (3000 - 10000) / (10 - 0) = -700

Y-intercept, b:
V = mt + b
10000 = (-700)(0) + b
b = 10000

Therefore, the linear equation for V is: 
V = -700t + 10000

Solve the Problem. -A Piece of Equipment Was Purchased by a Company for a Company