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.

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iwillanswer iwillanswer · Answer 1 · 2020-02-11T11:08:32+01:00

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