Answer: the value after 17 years is $3400
Explanation:
We would apply the formula,
y = ab^t
Where
a represents the initial amount of the car.
t represents the depreciation time.
From the information given
a = 36000
t = 5 years
Since after 5 years, the value depreciates by 0.5, then
y = 0.5 × 36000 = 18000
Therefore
18000 = 36000 × b^5
Dividing through by 36000, it becomes
0.5 = b^5
Raising both sides of the equation by 1/5, it becomes
0.5^(1/5) = b^5/5
b = 0.871
The equation becomes
y = 36000(0.871)^t
After 17 years, the value of the car would be
y = 36000(0.871)^17
y = $3440
y = $3400 to the nearest hundred dollar