document.write( "Question 1188014: The function f(x)=20(0.975)^x models the percentage of the surface sunlight, f(x), that reaches a depth of x feet beneath the surface of the ocean. Use the function f(x) to algebraically determine the depth, to the nearest hundredths of the foot, there is a 10% of surface sunlight. Use logarithms. \n" ); document.write( "

Algebra.Com's Answer #819059 by ikleyn(53937) $\"\"$ $\"About$

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\n" ); document.write( "The function f(x)=20(0.975)^x models the percentage of the surface sunlight, f(x),
\n" ); document.write( "that reaches a depth of x feet beneath the surface of the ocean.
\n" ); document.write( "Use the function f(x) to algebraically determine the depth, to the nearest hundredths
\n" ); document.write( "of the foot, there is a 10% of surface sunlight. Use logarithms.
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document.write( "According to the function, at the ocean surface x = 0, the intencity of sunlight is 20 units.\r\n" );
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document.write( "10% os 20 units is 2 units, so we write this equation\r\n" );
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document.write( "    2 = ,\r\n" );
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document.write( "divide by 20 both sides\r\n" );
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document.write( "     = \r\n" );
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document.write( "      0.1 = \r\n" );
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document.write( "take logarithm base 10 of both sides\r\n" );
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document.write( "    log(0.1) = x*log(0.975)\r\n" );
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document.write( "      -1     = x*log(0.975)\r\n" );
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document.write( "anf get\r\n" );
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document.write( "      x     =   = 90.95   (rounded as requested).\r\n" );
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document.write( "ANSWER.  This depth is  90.95 ft.\r\n" );
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