Answer:
$1400
Explanation:
You want the value of a car 18 years on if its initial value was $14,000 and its value is cut in half every 5.5 years.
Exponential model
The value of the car can be modeled by the exponential equation ...
value = (initial value) × (growth factor)^(t/(growth period))
where "growth period" is the period applicable to the "growth factor."
Application
Here, the problem statement tells us ...
- initial value = $14,000
- growth factor = 1/2
- growth period = 5.5 years
So, our exponential model is ...
value = 14,000·(1/2)^(t/5.5)
When t=18 years, this is ...
value = 14,000(1/2)^(18/5.5) = 14000(1/2)^(36/11) ≈ 14000·0.103469 ≈ 1449
The value after 18 years is about $1400.