After 4 half-lives, I ended up with 10 gram sample of Carbon-14. What was the original amount of Carbon-14
that I started with?

80g

Explanation:

The half - life is the time taken for half of radioactive substance to decay to half of its original composition.

After 4 half lives, the carbon - 14 sample is 10grams

 Now let us trace the decay of this substance;

At the 3rd  half life, it will have double the amount at the 4th half life;

                 2 x 10  = 20g

At the 2nd half life, there will be double the amount at the 3rd half life;

                20 x 2  = 40g

Originally, we are going to have;

               40 x 2 = 80g

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