A car was valued at $38,000 in the year 2003. The value depreciated to $11,000 by the year 2009. Assume that the car value continues to drop by the same percentage.

-What will the value be in the year 2013?

A new car was valued at $43,000, and it's value depreciated to $15,000 over the next 6 years. Use the exponential equation for depreciation to answer the following questions.

) What was the annual percent rate of depreciation, to 2 decimal places? Your answer will be a positive number.

ctm

Well, at this rate of depreciation, by the year 2013, the value of the car will probably be equal to the cost of a "free" bumper sticker. So, in other words, it will be worth approximately zilch! But hey, at least you'll have a cool sticker to show off.

To find the value of the car in the year 2013, we can use the concept of percentage depreciation.

Step 1: Find the depreciation rate per year.
To find the yearly depreciation rate, we need to calculate the percentage decrease in value from 2003 to 2009.

Value in 2003 = $38,000
Value in 2009 = $11,000

Total depreciation = Value in 2003 - Value in 2009 = $38,000 - $11,000 = $27,000

Depreciation per year = Total depreciation / Number of years = $27,000 / (2009 - 2003) = $27,000 / 6 = $4,500

Step 2: Calculate the value in 2013.
Since the car depreciates by the same percentage each year, the yearly depreciation rate remains constant.

To calculate the value in 2013, we need to subtract the total depreciation from the value in 2009.

Value in 2009 = $11,000
Total depreciation = $4,500 per year
Number of years from 2009 to 2013 = 2013 - 2009 = 4 years

Value in 2013 = Value in 2009 - (Total depreciation * Number of years)
= $11,000 - ($4,500 * 4)
= $11,000 - $18,000
= $-7,000

The value of the car in the year 2013 is estimated to be -$7,000. However, it is not possible for the value to be negative, so in this case, we can assume the car has no value or is considered worthless.

let the rate of depreciation be r

38000(1-r)^6 = 11000
(1-r)^6 = 11/38
1-r = (11/38)^(1/6)
1-r = .8133326
r = .186667

rate of depreciation is 18.67 %

so in 2012 it will be
38000(.8133326)^10 = $4813.55