Answer:
The fossil is 1860 years old.
Step-by-step explanation:
The equation for the amount of fossil has the following format:
![Q(t) = Q(0)e^{rt}](https://tex.z-dn.net/?f=Q%28t%29%20%3D%20Q%280%29e%5E%7Brt%7D)
In which Q(t) is the amount after t years, Q(0) is the initial amount and r is the rate of change.
Half-life of c-14 is 5730 years.
This means that ![Q(5730) = 0.5Q(0)](https://tex.z-dn.net/?f=Q%285730%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%7Brt%7D)
![0.5Q(0) = Q(0)e^{5730r}](https://tex.z-dn.net/?f=0.5Q%280%29%20%3D%20Q%280%29e%5E%7B5730r%7D)
![e^{5730r} = 0.5](https://tex.z-dn.net/?f=e%5E%7B5730r%7D%20%3D%200.5)
![\ln{e^{5730r}} = \ln{0.5}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B5730r%7D%7D%20%3D%20%5Cln%7B0.5%7D)
![5730r = \ln{0.5}](https://tex.z-dn.net/?f=5730r%20%3D%20%5Cln%7B0.5%7D)
![r = \frac{\ln{0.5}}{5730}](https://tex.z-dn.net/?f=r%20%3D%20%5Cfrac%7B%5Cln%7B0.5%7D%7D%7B5730%7D)
![r = -0.00012](https://tex.z-dn.net/?f=r%20%3D%20-0.00012)
So
![Q(t) = Q(0)e^{-0.00012t}](https://tex.z-dn.net/?f=Q%28t%29%20%3D%20Q%280%29e%5E%7B-0.00012t%7D)
How old is the fossil?
This is t for which
![Q(t) = 0.8Q(0)](https://tex.z-dn.net/?f=Q%28t%29%20%3D%200.8Q%280%29)
So
![Q(t) = Q(0)e^{-0.00012t}](https://tex.z-dn.net/?f=Q%28t%29%20%3D%20Q%280%29e%5E%7B-0.00012t%7D)
![0.8Q(0) = Q(0)e^{-0.00012t}](https://tex.z-dn.net/?f=0.8Q%280%29%20%3D%20Q%280%29e%5E%7B-0.00012t%7D)
![e^{-0.00012t} = 0.8](https://tex.z-dn.net/?f=e%5E%7B-0.00012t%7D%20%3D%200.8)
![\ln{e^{-0.00012t}} = \ln{0.8}](https://tex.z-dn.net/?f=%5Cln%7Be%5E%7B-0.00012t%7D%7D%20%3D%20%5Cln%7B0.8%7D)
![-0.00012t = \ln{0.8}](https://tex.z-dn.net/?f=-0.00012t%20%3D%20%5Cln%7B0.8%7D)
![t = -\frac{\ln{0.8}}{-0.00012}](https://tex.z-dn.net/?f=t%20%3D%20-%5Cfrac%7B%5Cln%7B0.8%7D%7D%7B-0.00012%7D)
![t = 1860](https://tex.z-dn.net/?f=t%20%3D%201860)
The fossil is 1860 years old.
Ions into a gas mixture according to their mass ratio q/m.
Answer:
82
Step-by-step explanation:
2*5 + 9*8 = 10 + 72 = 82
Answer:
2x^2(3x^2-2x-1)
Step-by-step explanation:
12x^4 - 8x^3 - 4x^2
everything is a multiple of 4 so divide the whole thing by 4
12x^4 - 8x^3 - 4x^2/4= 3x^4-2x^3-1x^2
write it in disturbed form
2(3x^4-2x^3-1x^2)
now if u see we can see that the X will be same, so we also have to factor it out and 2 is the exponent that all can give
2x^2(3x^2-2x-1)
Answer:
7 children
Step-by-step explanation:
$505-$115= $390
$390÷$65= 6
6+1= 7