An element with mass 730 grams decays by 27.6% per minute. How much of the element is remaining after 12 minutes, to the nearest 10th of a gram?
Accepted Solution
A:
Answer: 15.1 gramStep-by-step explanation:The exponential decay equation with rate of decay r in time period t is given by :-[tex]f(x)=A(1-r)^t[/tex], A is the initial value .Given: The initial mass of element= 730 gramsRate of decay= 27.6%=0.276Thus, the function represents the amount of element after t minutes is given by ;-[tex]f(x)=730(1-0.276)^x\\\\\Rightarrow\ f(x)=730(0.724)^x[/tex]Now, the function represents the amount of element after 12 minutes is given by ;-[tex]f(x)=730(0.724)^{12}\\\\\Rightarrow\ f(x)=15.1420841187\approx15.1\text{ grams}[/tex]Hence, 15.1 grams of element remains after 12 minutes.