B.) If the half-life of Carbon-14 is 5230 years and I start with 100 grams, how long will it take for the Carbon-14 to decay to 3.125 grams?

26150 years

Explanation:

First we need to determine the number of half lives -- not years -- it'll take for 100g (of any element) to decay to 3.125 g

First Half Life 100/2 = 50

Seconf Half Life 50/2 = 25

Third Half Life 25/2 = 12.5

Fourth Half Life 12.5/2 = 6.25

Fifth Half Life 6.25/2 = 3.125

So it'll take 5 half lives for 100g to decay to 3.125g.

If the Half Life of Carbon-14 is 5230 and it will take 5 half lives, to determine the number of years we just need to multiply 5*5230

5*5230 = 26150

This means that it will take 26150 years for 100g Carbon-14 to decay to 3.125g.

Hope this helps!