Depreciation involves the reduction in the value of a quantity
The rate of depreciation is about 13%
How to determine the equation
From the question, we have the following ordered pairs
(x,y) = {(0,9000) and (5,4500)}
The depreciation equation is represented as:
[tex]y = ab^x[/tex]
At (0,9000), we have:
[tex]ab^0 = 9000[/tex]
[tex]a = 9000[/tex]
At (5,4500), we have:
[tex]ab^5 = 4500[/tex]
This gives
[tex]9000b^5 = 4500[/tex]
Solve for b^5
[tex]b^5 = 0.5[/tex]
Take the 5th roots
[tex]b = 0.87[/tex]
So, we have:
[tex]y = ab^x[/tex]
[tex]y = 9000(0.87)^x[/tex]
The rate (r) is then calculated as:
[tex]1 -r = b[/tex]
This gives
[tex]r =1 - b[/tex]
[tex]r =1 - 0.87[/tex]
[tex]r =0.13[/tex]
Express as percentage
[tex]r= 13\%[/tex]
Hence, the rate of depreciation is about 13%
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