Answer:
y = - 5x
Step-by-step explanation:
Given that y varies directly with x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = - 10 when x = 2, thus
k =
=
= - 5
y = - 5x ← equation of variation
$2000 invested at 6.25% compounded annually will be worth $3,248 after 8 years.
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:
3sqrt(1) Approximation=3.16
Step-by-step explanation:
Break 10 into 3^2+1.
Sqrt(3^2+1) The 3 gets taken out of the radical
You get 3sqrt(1)
Answer:
![y=2x+5](https://tex.z-dn.net/?f=y%3D2x%2B5)
Step-by-step explanation:
![(5,0)](https://tex.z-dn.net/?f=%285%2C0%29)
Since the y-axis is cross on 5, that's the slope.
y=mx+5
To find x, let's use the formula;
![m=\frac{rise}{run}](https://tex.z-dn.net/?f=m%3D%5Cfrac%7Brise%7D%7Brun%7D)
![m=\frac{6}{3}=2](https://tex.z-dn.net/?f=m%3D%5Cfrac%7B6%7D%7B3%7D%3D2)