Nathan just bought a car. He models the value, V, in dollars, of the car after t years as V (t) = 21,000 (0.861) ^t. Based on this model, by what percent does the value of Nathan car decrease each year?

Question

Mathematics

Cutie Pie

12 September, 22:53

Nathan just bought a car. He models the value, V, in dollars, of the car after t years as V (t) = 21,000 (0.861) ^t. Based on this model, by what percent does the value of Nathan car decrease each year?

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Answers (1)

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Esmeralda · Answer 1

Value of the car is decreasing by 13.9% each year.

Step-by-step explanation:

This equation tells us V (t) is the value of the car after a certain time in years, $21,000 is the initial value of the car. What we need to focus on is on the 0.861 part of this equation. This means that the price of the car is worth 0.861 or 86.1% of what it was worth the year prior, this means that the price of the car is decreasing over time. By how much is it decreasing? Well if we consider 1 to mean 100% (since 100 / 100 = 1) then we have 100%-86.1%=13.9%. This means that the value of the car is decreasing 13.9% each year.