document.write( "Question 1172664: Element X is a radioactive isotope such that it’s mass decreases by 11% every year. If an experiment starts out with 530 grams of Element X, write a function to represent the mass of the sample after t years, where the quarterly rate of change can be found from a constant in the function. Round all coefficients in the function to four decimal places. Also, determine the percent rate of change per quarter, to the nearest hundredth of a percent.\r
\n" ); document.write( "\n" ); document.write( "Function: f(t)= ____ (___) ^ __\r
\n" ); document.write( "\n" ); document.write( "____ <- growth or decay?
\n" ); document.write( "____ % <- increase per quarter \n" ); document.write( "

Algebra.Com's Answer #797794 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "11% is lost each year, so each year the amount remaining is 100-11 = 89% of the amount at the beginning of the year. So the amount remaining gets multiplied by 89% = 0.89 each year.

\n" ); document.write( "So starting with 530 grams, after t years the amount remaining is

\n" ); document.write( " $\"530%280.89%29%5Et\"$

\n" ); document.write( "The portion remaining after a quarter of a year is, to a few decimal places,

\n" ); document.write( " $\"0.89%5E%281%2F4%29+=+0.971287\"$

\n" ); document.write( "So the decrease per quarter is

\n" ); document.write( " $\"1-.971287+=+0.028713\"$

\n" ); document.write( "or 2.87%.

\n" ); document.write( " \n" ); document.write( "

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