PreCalc help?

Question

For Tax purposes, rental houses are linearly depreciated over twenty seven and one half years. What would be a $110,000 house be worth after 3 years? (Hint: t= time of depreciation and V= value. Identify two points (t,V) and use them to construct a linear equation. Then compute V when t=3.

Answer choices are as follows:
$82,500
$98,000
$101,977
$107,000


All I know is that this is a linear equation. I don't understand what the "t" and the "V" are and how they are supposed to help me. Please show work.

Answer 1

You're right: this can be solved with a linear equation. (When you hear "linearly depreciated," think "linear equation," and think "linear graph.") In this case, house value (V) changes as time (t) changes, so V will be the dependent variable, and t the independent variable. Your graph will have V on the y-axis and t (in years) on the x-axis.

You know that now (in math lingo, that'd be "at time t=0") the house is worth $110,000, and in 27.5 years (t=27.5) the house is worth $0. So, find the equation of the line through (0, 110000) and (27.5, 0):

V = (-110000/27.5)*t + 110000

As you'd expect, the graph of this equation has a negative slope. (Here's some meaning to the slope: value goes down at a rate of -$110,000 over 27.5 years. So, the slope is -$110,000/(27.5 years).)

Now, to find the depreciated value of the house after 3 years, substitute 3 for t in the equation:

V = (-110000/27.5)*3 + 110000 = 98,000

So the value of the house after 3 years is $98,000.

Answer 2

V is the value of the house and t is the time so your function is V(t).

Since it's linear you need the slope and the y-intercept. The slope is easy to find:

m = change in V / change in t

change in V = $110,000 - $0

change in t = 0 years - 27.5 years

so m = 110,000 / -27.5 = -$4000/year

so V(t) = -4000 * t + y-intercept

V(t = 0 years) = -4000*(0) + y intercept = 110,000

y-int = 110,000

so

V(t) = 110,000 - 4000*t

V(t = 3 ) = 110,000 - 4000*3 = 110,000 - 12,000 = $98,000

Answer 3

If you want a easy, unsophisticated explanation, here it is. Since it is linear, it depreciates the same amount every year. Divide $110,000 by 27.5. Multiply this answer by 3 to get the depreciation for three years. Subtract this answer from $110,000. You already have several good formulas for this from other contributors.

Answer 4

V is the value of the house.
t is the time passed, in years.

V= 110000 - (110000/27.5)t

when t = 0, the house value is $110,000
when t = 27.5 the house value is $0

Use the above equation to solve for the value when t=3.

Answer 5

V (value)
t (time in years)

V = 110000 - t*110000/27.5

You do the rest