Consider the number line with the plotted square roots.
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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:
Upon rounding to nearest tenth, we will get:
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.