Video: Applications of Exponential Decay in a Real-World Context

Jennifer bought a new car for $20000 three years ago. If we assume that cars lose 13% of their value each year, how much is her car worth now, giving your answer to the nearest dollar?

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Video Transcript

Jennifer bought a car for 20000 dollars three years ago. If we assume that cars lose 13 percent of their value each year, how much is her car worth now giving your answer to the nearest dollar?

In order to calculate the new value, we need to identify three things from the question: firstly, the original value; secondly, the multiplier; and thirdly, the number of years. We will then substitute those three values into the formula or equation.

New value is equal to the original value multiplied by the multiplier to the power of the number of years. The original value of the car when Jennifer bought it was 20000 dollars. In order to find the multiplier, we need to work out whether the car has increased or decreased in value and by what percentage that has happened.

In this case, it is decreased by 13 percent. If the original value was a 100 percent and we have decreased by 13 percent, then we are now at 87 percent. Converting this to a decimal gives us 0.87. Therefore our multiplier is 0.87.

The final bit of information we need from the question is the number of years. In this case, Jennifer bought the car three years ago. Substituting all three of those values into the formula or equation gives us 20000 multiplied by 0.87 to the power of three.

Typing this into the calculator gives us a new value 13170.06. As six cents is less than 50, we ran down and our answer is 13170 dollars to the nearest dollar. At this stage, we could also work out how much the car has decreased by. In this case, 20000 minus 13170 gives us 6830. The car has decreased or depreciated by 6830 dollars.

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