Question

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 y=35795(0.83), where x represents the number of years since purchase and y represents the value (in dollars) of the car. How much will the car be worth five years after it is first purchased? How do you know? describe your calculation process.

Answer 1

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 $y=35795(0.83)^x$, 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 $x=5$ in our given equation as:

$y=35795(0.83)^5$

$y=35795\cdot (0.3939040643)$

$y=14099.79598$

Upon rounding to nearest tenth, we will get:

$y\approx 14099.8$

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 $y=a(1-r)^x$, where,

y = Final value after t years,

a = Initial value,

r = Decay rate in decimal form,

x= Time.

$17\%=\frac{17}{100}=0.17$

$y=35795(1-0.17)^x$

$y=35795(0.83)^x$