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?

Since

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

solve for $X$ in the equation

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