# Finding original amount in half-life problem

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?

• 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 6:05
• I know how to calculate half-life but don't know how to find the original amount. – jaykirby Jul 20 '13 at 6:06
• So, how do you calculate half-life? – Gerry Myerson Jul 20 '13 at 6:07
• 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. – Gerry Myerson Jul 20 '13 at 6:10
• The amount of the element has halved $\frac{1000}{1590}$ times. There was $\displaystyle 2^{\frac{1000}{1590}}\times 10g$ initially. – Angela Richardson Jul 20 '13 at 6:14

$$\text{Amount remaining} =\text{Original Amount} \times \bigg(\frac{1}{2}\bigg)^{\text{number of half lives}}$$
solve for $X$ in the equation
$$10 = X \times \bigg(\frac{1}{2}\bigg)^{\frac{1000}{1590}}$$