Answer:
2 h - 200 > 0
Step-by-step explanation:
Answer:
The axis of symmetry should be x = 2.
Step-by-step explanation:
:)
Answer:
<u>As per the graph we see:</u>
Domain is:
Range is:
Answer:
The age of the pottery bowl is 10523 years.
Step-by-step explanation:
Amount of substance:
The amount of a substance after t years is given by the following equation:
![A(t) = A(0)(1-r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281-r%29%5Et)
In which A(0) is the initial amount and r is the decay rate.
Half-life of C14.
Researching, the half-life of c-14 is 5730 years.
This means that:
![A(5730) = 0.5A(0)](https://tex.z-dn.net/?f=A%285730%29%20%3D%200.5A%280%29)
We use this to find r. So
![A(t) = A(0)(1-r)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%281-r%29%5Et)
![0.5A(0) = A(0)(1-r)^{5730}](https://tex.z-dn.net/?f=0.5A%280%29%20%3D%20A%280%29%281-r%29%5E%7B5730%7D)
![(1-r)^{5730} = 0.5](https://tex.z-dn.net/?f=%281-r%29%5E%7B5730%7D%20%3D%200.5)
![\sqrt[5730]{(1-r)^{5730}} = \sqrt[5730]{0.5}](https://tex.z-dn.net/?f=%5Csqrt%5B5730%5D%7B%281-r%29%5E%7B5730%7D%7D%20%3D%20%5Csqrt%5B5730%5D%7B0.5%7D)
![1 - r = 0.5^{\frac{1}{5730}}](https://tex.z-dn.net/?f=1%20-%20r%20%3D%200.5%5E%7B%5Cfrac%7B1%7D%7B5730%7D%7D)
![1 - r = 0.99987903922](https://tex.z-dn.net/?f=1%20-%20r%20%3D%200.99987903922)
So
![A(t) = A(0)(0.99987903922)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%280.99987903922%29%5Et)
Age of the pottery bowl:
We have that:
![A(t) = 0.28A(0)](https://tex.z-dn.net/?f=A%28t%29%20%3D%200.28A%280%29)
We have to find t. So
![A(t) = A(0)(0.99987903922)^t](https://tex.z-dn.net/?f=A%28t%29%20%3D%20A%280%29%280.99987903922%29%5Et)
![0.28A(0) = A(0)(0.99987903922)^t](https://tex.z-dn.net/?f=0.28A%280%29%20%3D%20A%280%29%280.99987903922%29%5Et)
![(0.99987903922)^t = 0.28](https://tex.z-dn.net/?f=%280.99987903922%29%5Et%20%3D%200.28)
![\log{(0.99987903922)^t} = \log{0.28}](https://tex.z-dn.net/?f=%5Clog%7B%280.99987903922%29%5Et%7D%20%3D%20%5Clog%7B0.28%7D)
![t\log{0.99987903922} = \log{0.28}](https://tex.z-dn.net/?f=t%5Clog%7B0.99987903922%7D%20%3D%20%5Clog%7B0.28%7D)
![t = \frac{\log{0.28}}{\log{0.99987903922}}](https://tex.z-dn.net/?f=t%20%3D%20%5Cfrac%7B%5Clog%7B0.28%7D%7D%7B%5Clog%7B0.99987903922%7D%7D)
![t = 10523.1](https://tex.z-dn.net/?f=t%20%3D%2010523.1)
So
The age of the pottery bowl is 10523 years.