The 1997 value of an object was $9500. In 2012, it was worth $5000. The annual percent of decay has been constant. Solve for the annual percent of decay. A. 4.37% B. 3.19% C. 2.19% D. 1.19%

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Mathematics

Joshua Bryan

17 April, 07:54

The 1997 value of an object was $9500. In 2012, it was worth $5000. The annual percent of decay has been constant. Solve for the annual percent of decay. A. 4.37% B. 3.19% C. 2.19% D. 1.19%

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Pedro Hurst · Answer 1

Let the anual rate of decay be k, then

A2 = A1 (1 + k) ^-n

5000 = 9500 (1 + k) ^ - (2012 - 1997) = 9500 (1 + k) ^-15

(1 + k) ^-15 = 5000/9500 = 0.5263

-15 log (1 + k) = log 0.5263

log (1 + k) = log 0.5263 / - 15 = 0.0186

1 + k = 10^0.0186 = 1.0437

k = 1.0437 - 1 = 0.0437 = 4.37%