# Sofia purchased a new car in 2007 for$34,000. The value of the car has been depreciating exponentially at a constant rate. If the value of the car was $16,200 in the year 2014, then what would be the predicted value of the car in the year 2021, to the nearest dollar?

2 answers

###### Question:

Sofia purchased a new car in 2007 for$34,000. The value of the car has been depreciating exponentially at a constant rate. If the value of the car was $16,200 in the year 2014, then what would be the predicted value of the car in the year 2021, to the nearest dollar?

## Answers

Answer:$7,718Step-by-step explanation:Given that :Cost of car in 2007 = $34000Cost of car in 2014 = $16200Predicted value of car in 2021Lets obtain the percentage Depreciation (d) :Worth (A) of car in 2014 = $16200Time (t) = 2014 - 2007 = 7 yearsInitial cost (I) = price in 2007A = I(1 - d/100)^716200 = 34000( 1 - d/100)^716200 = 34000(1 - 0.01d)^7(16200/34000)^1/7= 1 - 0.01d0.8995 = 1 - 0.01d0.01d = 1 - 0.8995d = 0.1005 /0.01d = 10.05Value of car in year 2021:t = 2021 - 2007 = 14 years A = I(1 - 10.05/100)^14A = 34000(1 - 0.1005)^14A = 34000(0.8995)^14A = 34000 * 0.2269950A =7717.83100Approximate worth = $7718

Answer: 7719Step-by-step explanation:

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