Answer:
32.894 seconds ≈ 33 seconds
Step-by-step explanation:
Function : [tex]Q(t)=Q_0 e^{-kt}[/tex]
The function models radioactive decay of krypton-91.
The decay constant k is approximately 0.07.
[tex]Q_0[/tex] denotes initial amount .
We are require to find How long will it take a quantity of krypton-91 to decay to 10% of its original amount
[tex]\Rightarrow 10\%\times Q_0[/tex]
[tex]\Rightarrow 0.10\times Q_0[/tex]
So, we neet to find t at which [tex]Q(t)=0.10 Q_0[/tex]
[tex]0.10 Q_0=Q_0 e^{-0.07t}[/tex]
[tex]0.10 =e^{-0.07t}[/tex]
Taking log both sides
[tex]\log0.10 =-0.07t \log e[/tex]
[tex]\log0.10 = -0.07t \times 0.434294481903[/tex]
[tex]-1 = -0.0304006137332t [/tex]
[tex]\frac{-1}{-0.0304006137332} = t [/tex]
[tex]32.894= t [/tex]
Thus it will take 32.894 seconds ≈ 33 seconds a quantity of krypton-91 to decay to 10% of its original amount.
