Faith purchased a new car in 1998 for $32,900. the value of the car has been depreciating exponentially at a constant rate. if the value of the car was $19,900 in the year 2003, then what would be the predicted value of the car in the year 2007, to the nearest dollar?

Respuesta :

The predicted value of the car in the year 2007 is 13310

Given the purchased value of new car in 1998 is  $ 32,900

The value of car was $ 19,900 in the year 2003

We need to find the value of the car in the year 2007

Let the predicted value be x

The exponentially constant rate in 2003

32900*x^5 = $19900 (∵ x^5 = 5 years difference that is 1998 to 2003 )

Now In year 2007

2007 = 32900*x^9

x = 0.9043

The predicted value of the car is 0.09043

But we want the predicted value in 2007

Therefore ,

In 2007 ≈ x = 13310.02

Rounding off to the nearest dollar is $13310

Therefore the predicted value of the car in 2007 is $13310

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