A car was valued at $35,000 in the year 1990. The value depreciated to $10,000 by the year 2003.
A) What was the annual rate of change between 1990 and 2003?(Round to 4 decimal places)
B)What is the correct answer to part A written in percentage form?
C)Assume that the car value continues to drop by the same percentage. What will the value be in the year 2006 ?(Round to the nearest 50 dollars)
This is just like your earlier post. In 13 years, the value was 10/35 its original worth. So, each year it decreased by a factor of
(10/35)^(1/13) = 0.9081
That should get you started.
To find the annual rate of change between 1990 and 2003, we can use the formula for the average annual rate of change:
Average Annual Rate of Change = (Ending Value - Starting Value) / Number of Years
A) Substituting the given values into the formula:
Average Annual Rate of Change = ($10,000 - $35,000) / (2003 - 1990)
= -$25,000 / 13, which is approximately -1923.0769 (rounded to 4 decimal places).
B) To express the answer in percentage form, we need to multiply the rate by 100:
Rate in Percentage Form = -1923.0769 * 100
= -192,307.69% (rounded to 4 decimal places).
C) Assuming that the car value continues to drop by the same percentage, we can calculate the value in the year 2006.
We know that the car's value in the year 2003 was $10,000, and the rate of change is approximately -1923.0769% per year.
To calculate the value in 2006, we first need to find the number of years from 2003 to 2006, which is 3 years.
Next, we multiply the current value ($10,000) by the rate of change in percentage form, expressed as a decimal ( -1923.0769% = -1923.0769 / 100 = -19.230769).
Value in 2006 = $10,000 * (1 - 0.19230769) ^ 3
= $10,000 * (1 - 0.19230769) * (1 - 0.19230769) * (1 - 0.19230769)
≈ $4184.70 (rounded to the nearest $50).
Therefore, the value of the car in the year 2006, assuming the same rate of change, would be approximately $4,200.