A new car is purchased for $15,000. In 10 years the same car has a scrap value of $1000.00. The rate of depreciation of its value is constant each year.
A determine an equation in the form y=mx+b to represent this situation
B how much is the car worth after 7 years.
The equation you use is:
final value = initial value * (rate of depreciation) ^ time
1000 = 15000(x)^10
x = .762765 or 76.2765%
value after 7 years is just:
15000(.762765)^7 = 2253.34
A) To determine the equation in the form y = mx + b, we need to first understand the depreciation pattern. We know that the value depreciates by a constant amount each year. Let's denote the initial value of the car as V0 and the value after t years as Vt.
The rate of depreciation per year (m) can be determined by dividing the change in value over the total number of years:
m = (V0 - Vt) / t
Now let's plug in the given values into the equation:
m = ($15,000 - $1,000) / 10
m = $14,000 / 10
m = $1,400
So, the equation for the depreciation of the car's value per year is:
y = $1,400x + b
B) To find the value of the car after 7 years (V7), we can substitute the value of x = 7 into the equation and solve for y:
y = $1,400(7) + b
However, to determine the value of b, we need additional information. We are given that the car is purchased for $15,000, but we don't know the initial value after 0 years (V0). Without this information, we cannot find the exact value of the car after 7 years.