document.write( "Question 1005212: The value of a car halves in 3 years. Find its annual rate of depreciation or loss in value. \n" ); document.write( "
Algebra.Com's Answer #621550 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
let \"+a+\" = the initial value of the car
\n" ); document.write( "Let \"+b+\" = the fraction that the value
\n" ); document.write( "gets reduced by each year
\n" ); document.write( "-------------------------
\n" ); document.write( "After 1st year:
\n" ); document.write( "\"+a+-+b%2Aa+=+a%2A%28+1+-+b+%29+\"
\n" ); document.write( "After 2nd year:
\n" ); document.write( "\"+a%2A%28+1+-+b+%29+-+b%2A%28+a%2A%28+1+-+b+%29+%29+=+a%2A%28+1+-+b+%29%2A%28+1+-+b+%29+\"
\n" ); document.write( "--------------------------
\n" ); document.write( "The rule is:
\n" ); document.write( "Current value of car=
\n" ); document.write( "\"+a%2A%28+1+-+b+%29%5En+\" after \"+n+\" years
\n" ); document.write( "-------------------------------
\n" ); document.write( "You are given that:
\n" ); document.write( "\"+a%2F2+=+a%2A%28+1+-+b+%29%5E3+\"
\n" ); document.write( "Divide both sides by \"+a+\"
\n" ); document.write( "\"+1%2F2+=+%28+1+-+b+%29%5E3+\"
\n" ); document.write( "Take the log of both sides
\n" ); document.write( "\"+log%28+1%2F2+%29+=+3%2Alog%28%28+1+-+b+%29%29+\"
\n" ); document.write( "\"+-.301+=+3%2Alog%28%28+1+-+b+%29%29+\"
\n" ); document.write( "\"+log%28%28+1+-+b+%29%29+=+-.10034+\"
\n" ); document.write( "\"+1+-+b+=+10%5E%28-.10034%29+\"
\n" ); document.write( "\"+1+-+b+=+.7937+\"
\n" ); document.write( "\"+b+=+.2063+\"
\n" ); document.write( "The annual depreciation is 20.63%
\n" ); document.write( "Hope I got it -you might want to get
\n" ); document.write( "another opinion on this
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