document.write( "Question 614077: A business estimates that the value V(t) of office equipment is decreasing according to the function V(t)=13200(4)^-0.14t, where t represents the number of years that have elapsed since the equipment was purchased, and V(t) is in dollars. After how many years will the value of the equipment be $3300? \n" ); document.write( "

Algebra.Com's Answer #386379 by nerdybill(7384) $\"\"$ $\"About$

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A business estimates that the value V(t) of office equipment is decreasing according to the function V(t)=13200(4)^-0.14t, where t represents the number of years that have elapsed since the equipment was purchased, and V(t) is in dollars. After how many years will the value of the equipment be $3300?
\n" ); document.write( ".
\n" ); document.write( "Given:
\n" ); document.write( " $\"V%28t%29=13200%284%29%5E-0.14t\"$
\n" ); document.write( "set V(t) t0 3300 and solve for t
\n" ); document.write( " $\"3300=13200%284%29%5E-0.14t\"$
\n" ); document.write( " $\"%283300%2F13200%29=%284%29%5E-0.14t\"$
\n" ); document.write( " $\"0.25+=+%284%29%5E-0.14t\"$
\n" ); document.write( "take log base 4 of both sides:
\n" ); document.write( " $\"log%284%2C0.24%29+=+-0.14t\"$
\n" ); document.write( " $\"log%280.24%29%2Flog%284%29+=+-0.14t\"$
\n" ); document.write( " $\"log%280.24%29%2F%28-0.14log%284%29%29+=+t\"$
\n" ); document.write( " $\"7.35319+=+t\"$
\n" ); document.write( "answer: 7.35 years \n" ); document.write( "

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