document.write( "Question 1038459: In 1997, there were 43.2 million people who used free weights. Assuming the use of free weights increases 6% annually, which equation can be used to predict the number of people using free weights t years from 1997?\r
\n" ); document.write( "\n" ); document.write( "p = 43.2(0.06)^t
\n" ); document.write( "p = 43.2(1.06)^t
\n" ); document.write( "p = 43.2(0.94)^t
\n" ); document.write( "p = 43.2(1.005)^t \n" ); document.write( "

Algebra.Com's Answer #653154 by solver91311(24713) $\"\"$ $\"About$

You can put this solution on YOUR website!
\r
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\n" ); document.write( "\n" ); document.write( "The amount next year is always the amount this year plus 6% times the amount this year.\r
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\n" ); document.write( "\n" ); document.write( "So lets look at what happens the first couple of years. Since t is the number of years after 1997, in 1997, t = 0, in 1998, t = 1, and so on.\r
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\r\n" );
document.write( "   t     Previous       Amount Added           Total\r\n" );
document.write( "-------------------------------------------------------------------------------------------------------------------\r\n" );
document.write( "   0      0             43.2                    0    +  43.2\r\n" );
document.write( "   1      43.2          43.2(0.06)             43.2  +  43.2(0.06) = 43.2(1.06)\r\n" );
document.write( "   2      43.2(1.06)    [43.2(1.06)](0.06)     43.2(1.06) + 43.2(1.06)(0.06) = 43.2(1.06)(1.06) = 43.2(1.06)²\r\n" );
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document.write( "

\r
\n" ); document.write( "\n" ); document.write( "I'll leave it to you to verify that for

the total is

.\r
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\n" ); document.write( "\n" ); document.write( "So, if we use the facts that

and

for any real numbers

, then we can clean up our chart thus:\r
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\r\n" );
document.write( "   t        Total\r\n" );
document.write( "-----------------------------\r\n" );
document.write( "   0        43.2(1.06)^0\r\n" );
document.write( "   1        43.2(1.06)^1\r\n" );
document.write( "   2        43.2(1.06)^2\r\n" );
document.write( "   3        43.2(1.06)^3\r\n" );
document.write( "        .\r\n" );
document.write( "        .\r\n" );
document.write( "        .\r\n" );
document.write( "   n        43.2(1.06)^n\r\n" );
document.write( "\r\n" );
document.write( "

\r
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\n" ); document.write( "\n" ); document.write( "John
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\n" ); document.write( "My calculator said it, I believe it, that settles it
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