Question

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%

Answer 1

D "4.19%"

Explanation:

Answer 2

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%