Question

In the year 2013, John's boat had a value of $16,000. When he bought the boat in 2007 he paid $29,000. If 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.

Answer 1

Answer: 7.47%.

Step-by-step explanation: To find the annual rate of change in the boat's value, we need to calculate the depreciation rate. The difference between the boat's value in 2007 ($29,000) and 2013 ($16,000) is $13,000. This represents the total depreciation over 6 years, giving an average depreciation of $2,166.67 per year. To find the percentage rate of change, we need to divide this by the original value and multiply by 100: $2,166.67/$29,000 x 100 = 7.47%. Therefore, the annual rate of change in the boat's value was approximately 7.47%.