g if 2 half-lives elapsed in a rock containing Carbon-14 and Nitrogen-14, what is the ratio of parent to daughter isotopes

The ratio of parent to daughter isotopes is .

Explanation:

We know that Carbon-14 decays in time and transforms into Nitrogen-14, being the latter the "daughter" of the first one. The decay of any isotope is represented by the following ordinary linear differential equation:

(Eq. 1)

Where:

- Rate of change of the isotope mass, measured in grams per year.

- Time constant, measured in years.

- Current mass of the isotope, measured in grams.

The solution of this differential equation is:

(Eq. 2)

Where:

- Time, measured in years.

- Initial mass of the isotope, measured in grams.

Time constant can be found as a function of half life. Please notice that half-life of Carbon-14 is 5760 years. The equation of time constant is:

(Eq. 3)

Where is the half-life of the isotope, measured in years.

If we know that and , then we have that:

Which means that 75 % of the original mass of Carbon-14 became Nitrogen-14. The parent-to-daughter ratio is:

The ratio of parent to daughter isotopes is .

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explanation:  

tariffs are a tax on anything that are imported from abroad. government use them to protect and boost their local industries and the thought is that they encourage consumers to buy local instead of importing and they will hope will protect jobs and economy in the country that implements them