Question

In 2004, Ryan bought a new boat for $32,500. The boat was worth $21,500 in the year 2008. If Ryan knows that the value of the boat depreciated linearly, what was the annual rate of change of the boat's value? Round your answer to the nearest hundredth if necessary.

A) 1.50%
B) 2.50%
C) -1.50%
D) -2.50%

Answer 1

The annual percentage rate of change in the boat's value was calculated as -8.46%, showing a yearly depreciation. This value does not match any of the options provided in the question, suggesting an error in the question or the multiple-choice options.

Step-by-step explanation:

To find the annual rate of change of the boat's value, we can use the formula for the slope of a linear equation, which is given by the change in value over the change in time. The initial value of the boat in 2004 was $32,500, and in 2008, the value was $21,500. This gives us a decrease in value of $32,500 - $21,500 = $11,000 over 4 years.

Now, we divide the total change in value by the total number of years to find the annual depreciation:

Annual rate of depreciation = $11,000 / 4 years = $2,750 per year.

To find the percentage rate of change, we take the annual depreciation and divide it by the initial value of the boat, then multiply by 100 to get a percentage:

Percentage rate of change = ($2,750 / $32,500) × 100 = 8.46% depreciation per year.

However, since the value of the boat is decreasing, we express this as a negative percentage, so the annual rate of change is -8.46%, which is not one of the options provided. Thus, we must conclude there may be an error in the question or the options provided.