We have been given that a new car, originally worth $35,795, depreciates at a rate of 17% per year. The value of the car can be represented by the equation
, where x represents the number of years since purchase and y represents the value (in dollars) of the car.
To find the value of car of after 5 years, we will substitute
in our given equation as:
![y=35795(0.83)^5](https://tex.z-dn.net/?f=y%3D35795%280.83%29%5E5)
![y=35795\cdot (0.3939040643)](https://tex.z-dn.net/?f=y%3D35795%5Ccdot%20%280.3939040643%29)
![y=14099.79598](https://tex.z-dn.net/?f=y%3D14099.79598)
Upon rounding to nearest tenth, we will get:
![y\approx 14099.8](https://tex.z-dn.net/?f=y%5Capprox%2014099.8)
Therefore, the car will be worth $14,099.8 after 5 years it is first purchased.
Since $14,099.8 is less than original value of car, therefore, we know hat value of car is depreciating and $14,099.8 is correct answer.
We also know that an exponential decay function is in form
, where,
y = Final value after t years,
a = Initial value,
r = Decay rate in decimal form,
x= Time.
![17\%=\frac{17}{100}=0.17](https://tex.z-dn.net/?f=17%5C%25%3D%5Cfrac%7B17%7D%7B100%7D%3D0.17)
![y=35795(1-0.17)^x](https://tex.z-dn.net/?f=y%3D35795%281-0.17%29%5Ex)
![y=35795(0.83)^x](https://tex.z-dn.net/?f=y%3D35795%280.83%29%5Ex)