Answer: The value of the car after 3 years is $5,333.333
And no, the relationship is not linear, is an exponential decay.
Step-by-step explanation:
We know that every year, the car loses 1/3 of its value.
So if the initial value of the car is V.
After one year, the new value of the car will be:
Value (1 year) = V - (1/3)*V = (2/3)*V
After another year, the value will be:
Value (2 years) = (2/3)*V - (1/3)*(2/3)*V = V*(2/3)^2
Ok, we already can see that this is an exponential decay.
(So no, this is not a linear relationship).
The value equation as a function of the number of years will be:
Value(N) = V*(2/3)^N
Then if the initial cost of a car is $18,000, and we want to know its value after 3 years, we need to replace V by $18,000 and N by 3 in the above equation:
Value(3) = $18,000*(2/3)^3 = $5,333.333
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