Radium has a half-life of 1,620 years. In how many years will a 1 kg sample of radium decay and reduce to 0.125 kg of radium? 1,620 years 3,240 years 4,860 years 6,480 years

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Well, I don't really understand this topic. How do you find the answer?

Ah okay. So half-life's just the amount of time it takes for half your initial amount to decay, right? If P is your principle amount, one half life leaves you with P/2, two half lives leave you with P/4, three with P/8, and so on. We express this mathematically as such: \[\Large A(t) = P*(1/2)^{t/H} \] where A(t) is the amount left after time t, P is your principle amount, and H is the length of time for your half life (in this case, 1,620 years). Though this may seem a bit foreign, it's really just the same as what we said above. Let's say one half life, or 1620 years have passed. t/H = 1, therefore, your amount = P/2. Exactly what we said above. In this question, we're actually given A(t) and we have to solve for t. Why don't you give it a try and see what you can get?

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