Answer:
a)
fraction of carbon−14 in a piece of charcoal remains after 14.0 years.
b)
fraction of carbon−14 in a piece of charcoal remains after 
c)
fraction of carbon−14 in a piece of charcoal remains after
.
Explanation:
The fraction of a radioactive isotope remaining at time t is given by:
![[A]=\frac{(\frac{1}{2})^t}{t_{\frac{1}{2}}}](https://tex.z-dn.net/?f=%5BA%5D%3D%5Cfrac%7B%28%5Cfrac%7B1%7D%7B2%7D%29%5Et%7D%7Bt_%7B%5Cfrac%7B1%7D%7B2%7D%7D%7D)
Taking log both sides:
![\log [A]=t\log[\frac{1}{2}]-\log [t_{\frac{1}{2}}]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3Dt%5Clog%5B%5Cfrac%7B1%7D%7B2%7D%5D-%5Clog%20%5Bt_%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D)
[A] = fraction at given time t
= half life of the carbon−14 =5,730 years
a)When , t = 14 years
![\log [A]=t\log[\frac{1}{2}]-\log [t_{\frac{1}{2}}]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3Dt%5Clog%5B%5Cfrac%7B1%7D%7B2%7D%5D-%5Clog%20%5Bt_%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D)
![\log [A]= 14 years\times (-3010)-\log [5,730 years]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3D%2014%20years%5Ctimes%20%28-3010%29-%5Clog%20%5B5%2C730%20years%5D)
![[A]=1.065\times 10^{-8}](https://tex.z-dn.net/?f=%5BA%5D%3D1.065%5Ctimes%2010%5E%7B-8%7D%20)
b)When , t = 
![\log [A]=t\log[\frac{1}{2}]-\log [t_{\frac{1}{2}}]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3Dt%5Clog%5B%5Cfrac%7B1%7D%7B2%7D%5D-%5Clog%20%5Bt_%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D)
![\log [A]= 1.900\times 10^4 years\times (-3010)-\log [5,730 years]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3D%201.900%5Ctimes%2010%5E4%20years%5Ctimes%20%28-3010%29-%5Clog%20%5B5%2C730%20years%5D)
![[A]=0.000\times 10^{-3} [/tex](https://tex.z-dn.net/?f=%5BA%5D%3D0.000%5Ctimes%2010%5E%7B-3%7D%20%5B%2Ftex%20)
c)When , t = 
![\log [A]=t\log[\frac{1}{2}]-\log [t_{\frac{1}{2}}]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3Dt%5Clog%5B%5Cfrac%7B1%7D%7B2%7D%5D-%5Clog%20%5Bt_%7B%5Cfrac%7B1%7D%7B2%7D%7D%5D)
![\log [A]= 1.0000\times 10^5 years\times (-3010)-\log [5,730 years]](https://tex.z-dn.net/?f=%5Clog%20%5BA%5D%3D%201.0000%5Ctimes%2010%5E5%20years%5Ctimes%20%28-3010%29-%5Clog%20%5B5%2C730%20years%5D)
![[A]=0.0000\times 10^{-4}](https://tex.z-dn.net/?f=%5BA%5D%3D0.0000%5Ctimes%2010%5E%7B-4%7D%20)
Answer:
When oceanic lithosphere and continental lithosphere collide, the dense oceanic lithosphere subducts beneath the less dense continental lithosphere.
Explanation:
Hope this helped Mark BRAINLEST!!!
Yes there is a great way to balance equation s
The Maillard reaction is a chemical reaction between an amino acid and a reducing sugar, usually requiring the addition of heat. Like caramelization, it is a form of non-enzymatic browning. The reactive carbonyl group of the sugar interacts with the nucleophilic amino group of the amino acid, and interesting but poorly characterized odor and flavor molecules result. This process accelerates in an alkaline environment because the amino groups do not neutralize. This reaction is the basis of the flavoring industry, since the type of amino acid determines the resulting flavor.
In the process, hundreds of different flavor compounds are created. These compounds in turn break down to form yet more new flavor compounds, and so on. Each type of food has a very distinctive set of flavor compounds that are formed during the Maillard reaction. It is these same compounds that flavor scientists have used over the years to create artificial flavors.