Answer:
C Infinitely Many Solutions
Step-by-step explanation:
i put the 2 equations into Desmos Graphing Calculator and they are the same line so it has infinitely many solutions.
Fu you ahole hhhhhhhhhhhhhhhhhhhhhhhhhh
I believe the answer your looking for is B.. good luck my friend!
160
Is the the answers r I did this before trust me
Using an exponential function, it is found that it takes 18.6 days for 80% of the material to decay.
The amount of a substance after t days is modeled by:
![A(t) = A(0)e^{-kt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29e%5E%7B-kt%7D)
In which:
- k is the decay rate, as a decimal.
- A(0) is the initial amount.
The half-life is of 8 days, hence
, and this is used to find k.
![A(t) = A(0)e^{-kt}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29e%5E%7B-kt%7D)
![0.5A(0) = A(0)e^{-8k}](https://tex.z-dn.net/?f=0.5A%280%29%20%3D%20A%280%29e%5E%7B-8k%7D)
![e^{-8k} = 0.5](https://tex.z-dn.net/?f=e%5E%7B-8k%7D%20%3D%200.5)
![\ln{e^{-8k}} = \ln{0.5}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B-8k%7D%7D%20%3D%20%5Cln%7B0.5%7D)
![-8k = \ln{0.5}](https://tex.z-dn.net/?f=-8k%20%3D%20%5Cln%7B0.5%7D)
![k = -\frac{\ln{0.5}}{8}](https://tex.z-dn.net/?f=k%20%3D%20-%5Cfrac%7B%5Cln%7B0.5%7D%7D%7B8%7D)
![k = 0.08664339757](https://tex.z-dn.net/?f=k%20%3D%200.08664339757)
Hence:
![A(t) = A(0)e^{-0.08664339757t}](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29e%5E%7B-0.08664339757t%7D)
The time it takes for 80% of the material to decay it t for which
, hence:
![0.2A(0) = A(0)e^{-0.08664339757t}](https://tex.z-dn.net/?f=0.2A%280%29%20%3D%20A%280%29e%5E%7B-0.08664339757t%7D)
![e^{-0.08664339757t} = 0.2](https://tex.z-dn.net/?f=e%5E%7B-0.08664339757t%7D%20%3D%200.2)
![\ln{e^{-0.08664339757t}} = \ln{0.2}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B-0.08664339757t%7D%7D%20%3D%20%5Cln%7B0.2%7D)
![-0.08664339757t = \ln{0.2}](https://tex.z-dn.net/?f=-0.08664339757t%20%3D%20%5Cln%7B0.2%7D)
![t = -\frac{\ln{0.2}}{0.08664339757}](https://tex.z-dn.net/?f=t%20%3D%20-%5Cfrac%7B%5Cln%7B0.2%7D%7D%7B0.08664339757%7D)
![t = 18.6](https://tex.z-dn.net/?f=t%20%3D%2018.6)
It takes 18.6 days for 80% of the material to decay.
To learn more about exponential functions, you can take a look at brainly.com/question/24906920