Question 1005212
let {{{ a }}} = the initial value of the car
Let {{{ b }}} = the fraction that the value 
gets reduced by each year
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After 1st year:
{{{ a - b*a = a*( 1 - b ) }}}
After 2nd year:
{{{ a*( 1 - b ) - b*( a*( 1 - b ) ) = a*( 1 - b )*( 1 - b ) }}}
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The rule is:
Current value of car=
{{{ a*( 1 - b )^n }}} after {{{ n }}} years
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You are given that:
{{{ a/2 = a*( 1 - b )^3 }}}
Divide both sides by {{{ a }}}
{{{ 1/2 = ( 1 - b )^3 }}}
Take the log of both sides
{{{ log( 1/2 ) = 3*log(( 1 - b )) }}}
{{{ -.301 = 3*log(( 1 - b )) }}}
{{{ log(( 1 - b )) = -.10034 }}}
{{{ 1 - b = 10^(-.10034) }}}
{{{ 1 - b = .7937 }}}
{{{ b = .2063 }}}
The annual depreciation is 20.63%
Hope I got it -you might want to get
another opinion on this