Start with the exponential decay model: V(t)=initial value × (annual multiplier)^t.
Annual multiplier = 1 − 0.17 = 0.83.
Initial value = 42000.
So the expression is: V(t) = 42000(0.83)^t, for t ≥ 0.
Write the exponential-decay formula for a car that loses 17% of its value each year. The initial value is $42,000, so V(t)=42000(0.83)^t gives the car's value t years after purchase.
Start with the exponential decay model: V(t)=initial value × (annual multiplier)^t.
Annual multiplier = 1 − 0.17 = 0.83.
Initial value = 42000.
So the expression is: V(t) = 42000(0.83)^t, for t ≥ 0.