Answer:
It will take approximately 3.34 hours for the drug to decay to 90% of the original dosage
Step-by-step explanation:
As suggested, we use the formula for exponential decay:
![A(t)=A_0\,e^{-k\,t}](https://tex.z-dn.net/?f=A%28t%29%3DA_0%5C%2Ce%5E%7B-k%5C%2Ct%7D)
From the given information, the half life of the drug in blood id 22 hours, so that means that it takes that number of hours to go from the initial value
, to a final value equal to
. Using this information we can find the decay rate "k" by solving for this parameter in the formula, and using the natural log function to bring the exponent down:
![A(t)=A_0\,e^{-k\,t}\\\frac{A_0}{2} =A_0\,e^{-k\,*22}\\\frac{A_0}{A_0*2} =e^{-k\,*22}\\\frac{1}{2} =e^{-k\,*22}\\ln(\frac{1}{2})=-k\,*22\\ k=-\frac{ln(\frac{1}{2})}{22} \\k=0.0315](https://tex.z-dn.net/?f=A%28t%29%3DA_0%5C%2Ce%5E%7B-k%5C%2Ct%7D%5C%5C%5Cfrac%7BA_0%7D%7B2%7D%20%3DA_0%5C%2Ce%5E%7B-k%5C%2C%2A22%7D%5C%5C%5Cfrac%7BA_0%7D%7BA_0%2A2%7D%20%3De%5E%7B-k%5C%2C%2A22%7D%5C%5C%5Cfrac%7B1%7D%7B2%7D%20%3De%5E%7B-k%5C%2C%2A22%7D%5C%5Cln%28%5Cfrac%7B1%7D%7B2%7D%29%3D-k%5C%2C%2A22%5C%5C%20k%3D-%5Cfrac%7Bln%28%5Cfrac%7B1%7D%7B2%7D%29%7D%7B22%7D%20%5C%5Ck%3D0.0315)
Now we use this value for the decay rate "k" to calculate how long it would take to decay to 90% of the original dose;
![A(t)=A_0\,e^{-0.0315\,t}\\0.9*A_0} =A_0\,e^{-0.0315\,t}\\\frac{0.9*A_0}{A_0} =e^{-0.0315\,t}\\0.9 =e^{-0.0315\,t}\\ln(0.9)=-0.0315\,t\\ t=-\frac{ln(0.9)}{0.0315} \\t=3.3447\,hours](https://tex.z-dn.net/?f=A%28t%29%3DA_0%5C%2Ce%5E%7B-0.0315%5C%2Ct%7D%5C%5C0.9%2AA_0%7D%20%3DA_0%5C%2Ce%5E%7B-0.0315%5C%2Ct%7D%5C%5C%5Cfrac%7B0.9%2AA_0%7D%7BA_0%7D%20%3De%5E%7B-0.0315%5C%2Ct%7D%5C%5C0.9%20%3De%5E%7B-0.0315%5C%2Ct%7D%5C%5Cln%280.9%29%3D-0.0315%5C%2Ct%5C%5C%20t%3D-%5Cfrac%7Bln%280.9%29%7D%7B0.0315%7D%20%5C%5Ct%3D3.3447%5C%2Chours)
Answer:
You would not subtract 3...
Step-by-step explanation:
It should be
2x- 8= 5x+3
subtract 5x from both sides,
then add 8 onto both sides, then you would get 0 on one side, and 11 on the other so you would have
-3=11 which equals
3.6
Answer:
it is a and c and b and e and also and f
Step-by-step explanation:
Dont know what you need to know??