Question

Answer only part c

A car was valued at $29,000 in the year 1991. The value depreciated to $14,000 by the year 2000.

A) What was the annual rate of change between 1991 and 2000?
r
= Correct Round the rate of decrease to 4 decimal places.

B) What is the correct answer to part A written in percentage form?
r
= Correct %.

C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2004 ?
value = $ Round to the nearest 50 dollars

Answer 1

The following frequency distribution depicts the scores on a math test. Find the class

midpoint of scores for the interval 95-99.

Explanation:

Answer 2

The value of the car in the year 2004, assuming it continues to depreciate at the same annual percentage rate, would be $10,150 when rounded to the nearest $50.

Based on the information provided:

- The car was valued at $29,000 in 1991.

- The value depreciated to $14,000 by the year 2000.

We have already calculated the annual rate of change as:

`\[ r = -0.0777 \]` (or -7.77% when expressed as a percentage)

Now, for part C, we want to calculate the value of the car in the year 2004, assuming the car continues to depreciate at the same annual percentage rate.

Since 4 years have passed from 2000 to 2004, we will apply the annual rate of decrease four times to the value of the car in the year 2000.

The formula for depreciation is:

`\[ \text{Future Value} = \text{Present Value} * (1 + r)^n \]`

Where:

-
`\( \text{Future Value} \)` is the value we want to find for the year 2004.

-
`\( \text{Present Value} \)` is the value of the car in the year 2000, which is $14,000.

-
`\( r \)` is the annual rate of decrease, which is -0.0777.

-
`\( n \)` is the number of years, which is 4.

Let's calculate the future value and then round it to the nearest 50 dollars.

The value of the car in the year 2004, assuming it continues to depreciate at the same annual percentage rate, would be $10,150 when rounded to the nearest $50.