The half-life of a radioactive kind of thallium is 5 minutes. How much will be left after 20 minutes, if you start with 933,392 grams of it?

Sure, here's how you can solve this problem:

1. First, understand that half-life is the time it takes for half of the radioactive substance to decay. In this case, the half-life of thallium is 5 minutes.

2. Next, determine how many half-lives have passed in the given time. In this case, 20 minutes have passed, so 20 minutes ÷ 5 minutes/half-life = 4 half-lives.

3. Now, calculate how much of the substance remains after each half-life. After one half-life, half of the original amount remains. After two half-lives, half of the remaining amount (or one-fourth of the original amount) remains. After three half-lives, half of that amount (or one-eighth of the original amount) remains, and so on.

4. So, after 4 half-lives, the remaining amount of thallium would be 933,392 grams * (1/2)^4 = 933,392 grams * 1/16 = 58,337 grams.

So, after 20 minutes, 58,337 grams of thallium would remain.