document.write( "Question 1097074: Plutonium-238 is used in bombs and power plants but is dangerously radioactive. It decays very slowly into nonradioactive materials. If you started with 300 grams today, a year from now you would still have 297.6 grams.
\n" ); document.write( "a) Construct an exponential function to describe the decay of plutonium-238 over time, rounding to three decimal places if necessary: P(t)=?
\n" ); document.write( "b) How much of the original 300 grams of plutonium-238 would be left after 60 years? After 600 years?
\n" ); document.write( "Round the answers to one decimal place. \n" ); document.write( "

Algebra.Com's Answer #711474 by jorel1380(3719) $\"\"$ $\"About$

You can put this solution on YOUR website!
a)The formula for exponential decay is P(t)=P(0)*e^-kt, where P(t) is the amount after time t, P(0) is the original amount, and k is a constant. In this instance:
\n" ); document.write( "297.6=300*e^-k
\n" ); document.write( ".992=e^-k
\n" ); document.write( "ln 0.992=ln e^-k=-k ln e=-k
\n" ); document.write( "k=0.00803217169726425903864943221985
\n" ); document.write( "So P(t)=P(0)e^-0.008t
\n" ); document.write( "b) after 60 years:
\n" ); document.write( "P(60)=300*e^-0.008(60)=185.277 gms
\n" ); document.write( "P(600)=300*e^-0.008(600)=2.42172345 gms
\n" ); document.write( "☺☺☺☺ \n" ); document.write( "

\n" );