The equation V = -2000t + 20,000 describes the value in dollars of a certain model of car after it is t years old. If a car is worth $14,000, find the age of the car.
V = -2000t + 20,000 = 14,000.
t = ?.
To find the age of the car when it is worth $14,000, we need to solve the given equation V = -2000t + 20,000 for t.
Step 1: Replace V with $14,000 in the equation:
$14,000 = -2000t + 20,000
Step 2: Rearrange the equation to isolate t:
-2000t = $14,000 - $20,000
-2000t = -$6,000
Step 3: Divide both sides of the equation by -2000 to solve for t:
t = (-$6,000) / (-2000)
Step 4: Simplify the right-hand side of the equation:
t = 3
Therefore, the age of the car is 3 years.