A radioactive substance decays according to the formula A=A0e^kt

where A0 is the initial amount of substance (in grams) A is the amount of substance (in grams) after t years

k is a constant The half-life of the substance is 10 years. If we begin with 20g of the substance, how much will be left after 5 years?

Without needing fancy formulas, we can conclude that after 10 years, half of the substance will be left. So, we can make our own formula:

amount remaining = 1 / 2^ (years/10)

So, after 5 years

amount remaining = 1 / 2^ (5/10)

amount remaining = 1 / 2^ (.5)

amount remaining = 1 / 1.414213562

amount remaining = 0.70711 * 20 grams

amount remaining = 14.1421356237 grams