Answer:
C. q Superscript 12
Step-by-step explanation:
![q \: Superscript \: 12 = {q}^{12} = { ({q}^{6})}^{2} \\](https://tex.z-dn.net/?f=%20q%20%20%5C%3A%20Superscript%20%5C%3A%20%2012%20%3D%20%20%7Bq%7D%5E%7B12%7D%20%3D%20%20%20%7B%20%28%7Bq%7D%5E%7B6%7D%29%7D%5E%7B2%7D%20%20%5C%5C%20)
6. addition property of equality (because 7 was added to each side)
7. A function has no repeating x values.....so the one that is not a function WILL HAVE repeating x values......and that would be C because it has repeating 2's
Thank you lord lord thank lord lord
Answer:
10.96 hours will take for 85% of the lead to decay.
Step-by-step explanation:
Suppose A represents the amount of Pb-209 at time t,
According to the question,
![\frac{dA}{dt}\propto A](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%5Cpropto%20A)
![\implies \frac{dA}{dt}=kA](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7BdA%7D%7Bdt%7D%3DkA)
![\int \frac{dA}{A}=\int kdt](https://tex.z-dn.net/?f=%5Cint%20%5Cfrac%7BdA%7D%7BA%7D%3D%5Cint%20kdt)
![ln|A|=kt+C_1](https://tex.z-dn.net/?f=ln%7CA%7C%3Dkt%2BC_1)
![A=e^{kt+C_1}](https://tex.z-dn.net/?f=A%3De%5E%7Bkt%2BC_1%7D)
![A=e^{C_1} e^{kt}](https://tex.z-dn.net/?f=A%3De%5E%7BC_1%7D%20e%5E%7Bkt%7D)
![\implies A=C e^{kt}](https://tex.z-dn.net/?f=%5Cimplies%20A%3DC%20e%5E%7Bkt%7D)
Let
be the initial amount,
![A_0=C e^{0} = C](https://tex.z-dn.net/?f=A_0%3DC%20e%5E%7B0%7D%20%3D%20C)
![\implies A=A_0 e^{kt}](https://tex.z-dn.net/?f=%5Cimplies%20A%3DA_0%20e%5E%7Bkt%7D)
Since, the half-life of 3.3 hours.
![\implies \frac{A_0}{2}=A_0 e^{3.3k}\implies e^{3.3k}=0.5\implies k=-0.21004](https://tex.z-dn.net/?f=%5Cimplies%20%5Cfrac%7BA_0%7D%7B2%7D%3DA_0%20e%5E%7B3.3k%7D%5Cimplies%20e%5E%7B3.3k%7D%3D0.5%5Cimplies%20k%3D-0.21004)
![\implies A=A_0 e^{-0.21004t}](https://tex.z-dn.net/?f=%5Cimplies%20A%3DA_0%20e%5E%7B-0.21004t%7D)
Here, ![A_0=1\text{ gram}](https://tex.z-dn.net/?f=A_0%3D1%5Ctext%7B%20gram%7D)
![A=(100-85)\% \text{ of }A_0=15\%\text{ of }A_0=0.15A_0](https://tex.z-dn.net/?f=A%3D%28100-85%29%5C%25%20%5Ctext%7B%20of%20%7DA_0%3D15%5C%25%5Ctext%7B%20of%20%7DA_0%3D0.15A_0)
By substituting the values,
![0.15A_0=A_0 e^{-0.21004t}](https://tex.z-dn.net/?f=0.15A_0%3DA_0%20e%5E%7B-0.21004t%7D)
![0.15=e^{-0.21004t}](https://tex.z-dn.net/?f=0.15%3De%5E%7B-0.21004t%7D)
![\implies t\approx 10.96\text{ hour}](https://tex.z-dn.net/?f=%5Cimplies%20t%5Capprox%2010.96%5Ctext%7B%20hour%7D)