Answer:
Thus, the pollutant concentration in lake will be reduced to 0.2% after 6.931471 days
Explanation:
From the information given:
A(t) = amount of pollutant for time (t)
A 4 billion cubic ft is the same as 4000 million cubic ft:
∴
The Initial amount of pollutant is ![A_o = (\dfrac{0.4}{100})\times 4000](https://tex.z-dn.net/?f=A_o%20%3D%20%28%5Cdfrac%7B0.4%7D%7B100%7D%29%5Ctimes%204000)
![A_o = 16 \ million \ cubic \ feet](https://tex.z-dn.net/?f=A_o%20%3D%2016%20%5C%20million%20%5C%20cubic%20%5C%20feet)
However;
the pollutant rate (input) = 400 × 0 = 0
the pollutant rate (output) = ![400( \dfrac{A(t)} {4000})](https://tex.z-dn.net/?f=400%28%20%5Cdfrac%7BA%28t%29%7D%20%7B4000%7D%29)
![= 1( \dfrac{A(t)} {10})](https://tex.z-dn.net/?f=%3D%201%28%20%5Cdfrac%7BA%28t%29%7D%20%7B10%7D%29)
The net rate = ![A'(t) = 0 - 1( \dfrac{A(t)} {10})](https://tex.z-dn.net/?f=A%27%28t%29%20%3D%200%20-%201%28%20%5Cdfrac%7BA%28t%29%7D%20%7B10%7D%29)
![\implies A'(t) = - 1( \dfrac{A(t)} {10})](https://tex.z-dn.net/?f=%5Cimplies%20A%27%28t%29%20%3D%20-%201%28%20%5Cdfrac%7BA%28t%29%7D%20%7B10%7D%29)
![\implies \dfrac{1}{A(t)}A'(t) = -(\dfrac{1}{10})](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%7B1%7D%7BA%28t%29%7DA%27%28t%29%20%3D%20-%28%5Cdfrac%7B1%7D%7B10%7D%29)
![\implies \int (\dfrac{1}{A(t)}A'(t) ) dt = \int -(\dfrac{1}{10}) dt](https://tex.z-dn.net/?f=%5Cimplies%20%5Cint%20%28%5Cdfrac%7B1%7D%7BA%28t%29%7DA%27%28t%29%20%29%20dt%20%3D%20%5Cint%20%20-%28%5Cdfrac%7B1%7D%7B10%7D%29%20dt)
![\implies In (A(t)) = -(\dfrac{1}{10})t + c](https://tex.z-dn.net/?f=%5Cimplies%20In%20%28A%28t%29%29%20%3D%20-%28%5Cdfrac%7B1%7D%7B10%7D%29t%20%2B%20c)
![\implies A(t) = e^{-(\dfrac{1}{10})t+c}](https://tex.z-dn.net/?f=%5Cimplies%20%20A%28t%29%20%3D%20e%5E%7B-%28%5Cdfrac%7B1%7D%7B10%7D%29t%2Bc%7D)
![\implies A(t) = Ce^{-\dfrac{1}{10}^t}](https://tex.z-dn.net/?f=%5Cimplies%20A%28t%29%20%3D%20Ce%5E%7B-%5Cdfrac%7B1%7D%7B10%7D%5Et%7D)
A(0) = 16
![\implies Ce^{ -(1/20)^0} = 16 \\ \\ C = 16](https://tex.z-dn.net/?f=%5Cimplies%20Ce%5E%7B%20-%281%2F20%29%5E0%7D%20%3D%2016%20%5C%5C%20%5C%5C%20%20C%20%3D%2016)
![\implies A(t) = 16e^{(-1/10)t}](https://tex.z-dn.net/?f=%5Cimplies%20A%28t%29%20%3D%2016e%5E%7B%28-1%2F10%29t%7D)
![0.2\% \ pollutant = (\dfrac{0.2}{100})*4000 =8 \ million \ cubic \ feet](https://tex.z-dn.net/?f=0.2%5C%25%20%5C%20pollutant%20%3D%20%28%5Cdfrac%7B0.2%7D%7B100%7D%29%2A4000%20%3D8%20%5C%20%20million%20%20%5C%20cubic%20%20%5C%20feet)
A(t) = 8
![\implies 16e^{(-1/10)t}= 8 \\ \\ \implies e^{1/10)t} = 2 \\ \\ (\dfrac{1}{10} )^t = In(2) \\ \\ t = 10\ In(2) \\ \\ \mathbf{ t = 6.931471}](https://tex.z-dn.net/?f=%5Cimplies%2016e%5E%7B%28-1%2F10%29t%7D%3D%208%20%20%5C%5C%20%5C%5C%20%5Cimplies%20%20e%5E%7B1%2F10%29t%7D%20%3D%202%20%5C%5C%20%5C%5C%20%20%28%5Cdfrac%7B1%7D%7B10%7D%20%29%5Et%20%3D%20In%282%29%20%20%5C%5C%20%5C%5C%20%20t%20%3D%2010%5C%20In%282%29%20%5C%5C%20%5C%5C%20%5Cmathbf%7B%20t%20%3D%206.931471%7D)
Answer:
hhtrdtrdcg hnhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh
Explanation:
The orbitals of a particular atom are not the only allowed states that an electron can take on in the atom. They are the only stable states of the atom, meaning that when an electron settles down to a particular state in an atom, it must be in one of the orbital states.
Answer: When completely decomposed it will be -11 kJ
D. Because it shows the best definition of matter