A radioactive substance has a decay rate of 0.073 per minute. How many grams of a 120 gram sample will remain radioactive after 30 minutes? Round the answer to the nearest tenth of a gram, and do not include the unit in your answer.
Accepted Solution
A:
Answer:13.4 grams of a 120 gram sample will remain radioactive after 30 minutes.Step-by-step explanation:Given : A radioactive substance has a decay rate of 0.073 per minute. To find : How many grams of a 120 gram sample will remain radioactive after 30 minutes? Solution : Using decaying formula, [tex]y(t)=y_o e^{-rt}[/tex]Where, [tex]y_o=120[/tex] is the initial amountr=0.073 is the decay rate t=30 minute is the timeSubstitute the value in the formula,[tex]y(30)=120\times e^{-0.073\times 30}[/tex][tex]y(30)=120\times e^{-2.19}[/tex][tex]y(30)=120\times 0.1119[/tex][tex]y(30)=13.428[/tex][tex]y(30)=13.4[/tex]Therefore, 13.4 grams of a 120 gram sample will remain radioactive after 30 minutes.