document.write( "Question 1041927: The purchasing power of A dollars after t years of r% inflation is given by the model P = Ae^-rt. Assume the inflation rate is currently 3.8%. How long will it take for the purchasing power of $1.00 to be worth $0.76? Round the answer to the nearest hundredth. \n" ); document.write( "

Algebra.Com's Answer #657040 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"+P+=+A%2Ae%5E%28-r%2At%29+\"$
\n" ); document.write( " $\"+A+\"$ = amount in dollars before inflation
\n" ); document.write( " $\"+P+\"$ = amount in dollars after inflation
\n" ); document.write( " $\"+r+\"$ = % inflation
\n" ); document.write( " $\"+t+\"$ = time in years of r% inflation
\n" ); document.write( "--------------------------------------
\n" ); document.write( " $\"+r+=+.038+\"$
\n" ); document.write( " $\"+A+=+1+\"$
\n" ); document.write( " $\"+P+=+.76+\"$
\n" ); document.write( "-----------------
\n" ); document.write( " $\"+P+=+A%2Ae%5E%28-r%2At%29+\"$
\n" ); document.write( " $\"+.76+=+1%2Ae%5E%28-+.038t+%29+\"$
\n" ); document.write( "Take the natural log of both sides
\n" ); document.write( " $\"+ln%28+.76+%29+=+-.038t+\"$
\n" ); document.write( " $\"+-.27444+=-.038t+\"$
\n" ); document.write( " $\"+t+=+7.222+\"$
\n" ); document.write( "It will take 7.22 yrs
\n" ); document.write( "--------------------
\n" ); document.write( "check:
\n" ); document.write( " $\"+.76+=+1%2Ae%5E%28-+.038t+%29+\"$
\n" ); document.write( " $\"+.76+=+1%2Ae%5E%28-+.038%2A7.222+%29+\"$
\n" ); document.write( " $\"+.76+=+e%5E%28+-.2744+%29+\"$
\n" ); document.write( " $\"+.76+=+.76003+\"$
\n" ); document.write( "close enough \n" ); document.write( "

\n" );