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
The value of car after 3 years is $5333
It is an exponential relationship.
Given :
Every year after a new car is purchased, it loses 1/3 of its value
one third of value is depreciated. So, [tex]1-\frac{1}{3}= \frac{2}{3}[/tex]
two third of the value is remaining after depreciation .
Let's say that the new car costs $18,000.
The value of cost of new car after 1 year is [tex]\frac{2}{3} \cdot 18000[/tex]
Now again the car value is depreciated on second year
The value of cost of car after 2 years is [tex]\frac{2}{3} \cdot \frac{2}{3} \cdot 18000[/tex]
The value of cost of car after 3 years is [tex]\frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} \cdot 18000[/tex]
The cost of car after 'n' years is
[tex](\frac{2}{3})^n \cdot 18000[/tex]
Its an exponential relationship.
because 2/3 is multiplied 'n' times .
The value of car after 3 years is
[tex]\frac{2}{3} \cdot \frac{2}{3} \cdot \frac{2}{3} \cdot 18000=5333[/tex]
Learn more : brainly.com/question/24218291
