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Say the half-life of an element is 1590 years. If 10g of the element is left after 1000 years, how much was there originally?

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  • $\begingroup$ What do you know about this kind of problem? Have you not been shown some formulas that might be useful? $\endgroup$ – Gerry Myerson Jul 20 '13 at 6:05
  • $\begingroup$ I know how to calculate half-life but don't know how to find the original amount. $\endgroup$ – jaykirby Jul 20 '13 at 6:06
  • $\begingroup$ So, how do you calculate half-life? $\endgroup$ – Gerry Myerson Jul 20 '13 at 6:07
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    $\begingroup$ What does $k$ stand for? what does $t$ stand for? How would you use that formula? what would you have to know, and what computation would you do? Full sentences, please. $\endgroup$ – Gerry Myerson Jul 20 '13 at 6:10
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    $\begingroup$ The amount of the element has halved $\frac{1000}{1590}$ times. There was $\displaystyle 2^{\frac{1000}{1590}}\times 10g$ initially. $\endgroup$ – Angela Richardson Jul 20 '13 at 6:14
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Since

$$\text{Amount remaining} =\text{Original Amount} \times \bigg(\frac{1}{2}\bigg)^{\text{number of half lives}} $$

solve for $X$ in the equation

$$10 = X \times \bigg(\frac{1}{2}\bigg)^{\frac{1000}{1590}}$$

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