A stereo is bought for $1500 and sold 4 years later for $800.
a) Find the depreciation equation.
b) Assuming the depreciation is linear, find the value of the stereo after the first five years of ownership.
value = mt + 1500
when t = 4, value = 800
800 = 4m + 1500
4m = -700
m = -175
value = -175t + 1500
plug in t = 5 to find value
a. Vt = Vo - d*T*Vo.
Vt = Value after time t.
Vo = Initial value.
d = Depreciation rate per year expressed as a decimal.
1500 - 4d*1500 = 800, d = 0.117/yr.
b. V = 1500 - 0.117*5*1500 =
a) To find the depreciation equation, we can use the formula for the equation of a straight line: y = mx + b, where y represents the value of the stereo and x represents the number of years of ownership.
Let's assign the value of the stereo to y and the number of years to x. Initially, the value of the stereo is $1500, so we have the point (0, 1500). After 4 years, the stereo is sold for $800, giving us the point (4, 800).
Using these two points, we can find the slope of the line (m) using the formula:
m = (change in y) / (change in x)
m = (1500 - 800) / (0 - 4)
m = 700 / -4
m = -175
Now, we can substitute the slope (m) into the equation and solve for the y-intercept (b):
1500 = -175(0) + b
b = 1500
Therefore, the depreciation equation is y = -175x + 1500.
b) If we assume that the depreciation is linear, we can use the depreciation equation to find the value of the stereo after the first five years of ownership (x = 5).
Plugging x = 5 into the equation, we get:
y = -175(5) + 1500
y = -875 + 1500
y = 625
Therefore, the value of the stereo after the first five years of ownership is $625.
a) To find the depreciation equation, we need to determine the rate at which the stereo is depreciating per year. We can subtract the selling price from the initial purchase price and divide it by the number of years:
Depreciation per year = (Initial purchase price - Selling price) / Number of years
Given:
Initial purchase price (P) = $1500
Selling price (S) = $800
Number of years (N) = 4
Depreciation per year = (1500 - 800) / 4 = 700 / 4 = $175
Therefore, the depreciation equation for this stereo is:
Depreciation = $175 * Number of years
b) Assuming linear depreciation, we can find the value of the stereo after the first five years by using the depreciation equation we found in part a.
Number of years (N) = 5
Depreciation = $175 * 5 = $875
To find the value of the stereo after the first five years, we subtract the depreciation from the initial purchase price:
Value after five years = Initial purchase price - Depreciation
Value after five years = $1500 - $875 = $625
Therefore, the value of the stereo after the first five years of ownership is $625.