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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What do you know about this kind of problem? Have you not been shown some formulas that might be useful? – Gerry Myerson Jul 20 '13 at 06:05
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I know how to calculate half-life but don't know how to find the original amount. – jaykirby Jul 20 '13 at 06:06
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So, how do you calculate half-life? – Gerry Myerson Jul 20 '13 at 06:07
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ln(fraction remaining) = -kt – jaykirby Jul 20 '13 at 06:08
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1What 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. – Gerry Myerson Jul 20 '13 at 06:10
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k stands for rate constant and t for time. to use the formula you would need to know at least 2 of the 3 unknowns. – jaykirby Jul 20 '13 at 06:11
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1The amount of the element has halved $\frac{1000}{1590}$ times. There was $\displaystyle 2^{\frac{1000}{1590}}\times 10g$ initially. – Angela Pretorius Jul 20 '13 at 06:14
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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
$$10 = X \times \bigg(\frac{1}{2}\bigg)^{\frac{1000}{1590}}$$
Ink
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