Find a linear model for the depreciated value V of the tractor t years after it was purchased.

Question

a farmer buys a new tractor for $155,000 and assumes that it will have a trade-in value of $79,000 after 10 years. The farmer uses a constant rate of depreciation to determine the annual value of the tractor.

Answer 1

Linear model :

 

y = mx + b

 

 

The initial cost of the tractor is 155,000

 

Let's make

x = t = years after tractor was purchased

y = V(t) = value of the tractor in thousand dollars (i.e 79 = $79,000 ; for simpler math)

 

V(t) = mt + b

 

The initial cost, at t= 0 gives the y-intercept

V(0) = 155 = m(0) + b

then b = 155

 

We are given the point (10, 79) to find the slope, m

V(10) = 79 = m(10) + 155

79 - 155 = m(10)

 

-76 = m(10)

-76/10 = m

-7.6 = m

 

V(t) = -7.6t + 155