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at the band's peak of popularity , a signed black diamond poster sold for $500. three years later, the band was almost forgotten, and the poster was worth only $10. what is the annual rate of depreciation for the poster

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The answer to this question would be 72.8%
In this case, you are given the initial price($500), the final price($10) and the elapsed time(3 years). You are asked to find the annual or yearly rate of depreciation. The calculation should be:

Final price= initial price * (100%- depreciation rate)^(elapsed time/time unit of depreciation)
$10= $500 * (100% - depreciation rate) ^(3/1)
(100%- depreciation rate)^3= 10/500= 1/50
depreciation rate= 1/3.68 -100 = -72.8%

Every year the poster is losing 72.8% value(the value is turned into 27.2%)

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