In the year 2011, Ryan's boat had a value of $23,000. When he bought the boat in 2004 he paid $26,500. 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.

The constant amount of depreciation in the value of boat per year is $ 500

Solution:

When he bought the boat in 2004 he paid $26,500

Therefore,

Initial value in 2004 = $ 26500

In the year 2011, Ryan's boat had a value of $23,000

Value in 2011 = $ 23000

The value of the boat depreciated linearly

If the boat depreciation is linear, then the amount by which the value of boat depreciates must be constant.

Let x be the constant depreciation in the value of boat per year

Then we can say,

Value in 2011 = Initial value in 2004 - nx

Here, "n" is the number of years

2011 - 2004 = 7 years

Therefore,

23000 = 26500 - 7x

7x = 26500 - 23000

7x = 3500

Divide both sides by 7

x = 500

Thus the rate of depreciation per year is $ 500