Respuesta :
Answer:t=9.6 minutes
Step-by-step explanation:
Given
mass of element is [tex]A_o=740\ gm[/tex]
Decay rate [tex]r=28.4\%\ \text{per minute}[/tex]
and we know
Amount of exponential decay is given by
[tex]A=A_o[1-r]^t[/tex]
Where [tex]A_0=\text{Initial amount}[/tex]
[tex]\text{A=Accumulated amount}[/tex]
[tex]\text{r=rate}[/tex]
[tex]\text{t=time}[/tex]
Substituting values we get
[tex]\Rightarrow 30=740[1-0.284]^t[/tex]
[tex]\Rightarrow \dfrac{30}{740}=0.716^t[/tex]
[tex]\Rightarrow 0.0405=0.716^t[/tex]
taking log both sides we get
[tex]\Rightarrow\ \ln (0.0405)=t\times \ln (0.716)[/tex]
[tex]\Rightarrow t=\dfrac{\ln (0.0405)}{\ln (0.716)}[/tex]
[tex]\Rightarrow t=9.598\approx 9.6\ \text{minutes}[/tex]
