Answer:
18.37 is the answer so it should be 18.4
Step-by-step explanation:
Answer:
It would take 24 minutes for the element to decay to 50 grams
Step-by-step explanation:
The equation for the amount of the element present, after t minutes, is:
![Q(t) = Q(0)e^{-rt}](https://tex.z-dn.net/?f=Q%28t%29%20%3D%20Q%280%29e%5E%7B-rt%7D)
In which Q(X) decays radioactively with a half life of 12 minutes.(0) is the initial amount and r is the rate it decreases.
Half life of 12 minutes
This means that ![Q(12) = 0.5Q(0)](https://tex.z-dn.net/?f=Q%2812%29%20%3D%200.5Q%280%29)
So
![Q(t) = Q(0)e^{-rt}](https://tex.z-dn.net/?f=Q%28t%29%20%3D%20Q%280%29e%5E%7B-rt%7D)
![0.5Q(0) = Q(0)e^{-12r}](https://tex.z-dn.net/?f=0.5Q%280%29%20%3D%20Q%280%29e%5E%7B-12r%7D)
![e^{-12r} = 0.5](https://tex.z-dn.net/?f=e%5E%7B-12r%7D%20%3D%200.5)
![\ln{e^{-12r}} = \ln{0.5}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B-12r%7D%7D%20%3D%20%5Cln%7B0.5%7D)
![-12r = \ln{0.5}](https://tex.z-dn.net/?f=-12r%20%3D%20%5Cln%7B0.5%7D)
![12r = -\ln{0.5}](https://tex.z-dn.net/?f=12r%20%3D%20-%5Cln%7B0.5%7D)
![r = -\frac{\ln{0.5}}{12}](https://tex.z-dn.net/?f=r%20%3D%20-%5Cfrac%7B%5Cln%7B0.5%7D%7D%7B12%7D)
![r = 0.05776](https://tex.z-dn.net/?f=r%20%3D%200.05776)
If there are 200 grams of Element X, how long, to the nearest tenth of a minute, would it take the element to decay to 50 grams?
This is t when Q(t) = 50. Q(0) = 200.
![Q(t) = Q(0)e^{-rt}](https://tex.z-dn.net/?f=Q%28t%29%20%3D%20Q%280%29e%5E%7B-rt%7D)
![50 = 200e^{-0.05776t}](https://tex.z-dn.net/?f=50%20%3D%20200e%5E%7B-0.05776t%7D)
![e^{-0.05776t} = 0.25](https://tex.z-dn.net/?f=e%5E%7B-0.05776t%7D%20%3D%200.25)
![\ln{e^{-0.05776t}} = \ln{0.25}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B-0.05776t%7D%7D%20%3D%20%5Cln%7B0.25%7D)
![-0.05776t = \ln{0.25}](https://tex.z-dn.net/?f=-0.05776t%20%3D%20%5Cln%7B0.25%7D)
![0.05776t = -\ln{0.25}](https://tex.z-dn.net/?f=0.05776t%20%3D%20-%5Cln%7B0.25%7D)
![t = -\frac{\ln{0.25}}{0.05776}](https://tex.z-dn.net/?f=t%20%3D%20-%5Cfrac%7B%5Cln%7B0.25%7D%7D%7B0.05776%7D)
![t = 24](https://tex.z-dn.net/?f=t%20%3D%2024)
It would take 24 minutes for the element to decay to 50 grams
Answer: X= -5
Step-by-step explanation:
Answer:
-19b + 78
Step-by-step explanation:
We multiply by 10 to make it easier
13b+78-32b
-19b + 78
20 feet should be the correct answer. not sure if there's any choices