Business equipment is often depreciated using the double declining-balance method. In this method, a piece of equipment with a life expectancy of N years, costing C dollars, will depreciate to a value of V dollars in n years, where n is given by the formula: $n = \frac { \log V - \log C } { \log \left( 1 - \frac { 2 } { N } \right) }$ A computer that cost $10,000 has a life expectancy of 5 years. If it has depreciated to a value of $2,000, how old is it? Round the answer to the nearest tenth of the year.
A)3.2 years old
B)2.2 years old
C)1.9 years old
D)2.5 years old
E)2.8 years old

Question

Quizplus · Accepted Answer

The formula given is $n = \frac { \log V - \log C } { \log \left( 1 - \frac { 2 } { N } \right) }$. Substituting the given values: $C = 10000$, $V = 2000$, and $N = 5$, we get $n = \frac { \log 2000 - \log 10000 } { \log \left( 1 - \frac { 2 } { 5 } \right) }$. Calculating this gives $n \approx 3.2$ years.

Business Equipment Is Often Depreciated Using the Double Declining-Balance Method n=log⁡V−log⁡Clog⁡(1−2N)n = \frac { \log V - \log C } { \log \left( 1 - \frac { 2 } { N } \right) }n=log(1−N2​)logV−logC​

Business Equipment Is Often Depreciated Using the Double Declining-Balance Method $n = \frac { \log V - \log C } { \log \left( 1 - \frac { 2 } { N } \right) }$