A 650 washing machine in a Laundromat is depreciated for tax purposes at a rate of 65 per year. Find a function for the depreciated value of the washing machine as it varies with time. When does the depreciated value reach 0?
Solution:-
Use the slope-intercept form of an equation to develop a model for the given data.
The independent variable is the time in years, t, and the dependent variable is the price of the washing machine, V.
Read the problem statement and find the slope, or the rate of depreciation per year.
m = -65
To find the equation of the line in slope-intercept form, notice that the depreciation per year is the coefficient of the time t, and the initial value of the machine, 650, is the constant term.
The equation of the line in slope-intercept form is V = 650 – 65t.
To find how long it takes for the washing machine to depreciate to 0, substitute 0 for V and solve for t.
V = 650 – 65t
0= 650 – 65t
65t = 650
t = 10
Therefore, it takes 10 years for the washing machine to depreciate to 0.