You bought a new car for $26,500 in 2005, and the value of the car depreciates by $900 each year. Find a formula for V, the value of the car, in terms of t, the number of years since 2005.
V = -900t + 26500
To find a formula for the value of the car, V, in terms of the number of years since 2005, t, we can start by defining the initial value of the car.
Given that the car was bought for $26,500 in 2005, this serves as the initial value, also known as the principal, P. Now, let's define the rate of depreciation.
The value of the car depreciates by $900 each year. Since the value is decreasing, we can consider this as a negative rate of change, which we can denote as -900. Now, let's incorporate this into the formula.
Using the basic compound interest formula:
V = P + rt
where V represents the value of the car, P is the initial value, r is the rate of change (depreciation rate), and t is the number of years.
Substituting the values we have:
V = 26,500 - 900t
Therefore, the formula for the value of the car, V, in terms of the number of years since 2005, t, is V = 26,500 - 900t.