Answer Key for Worksheet 3-3 on Half-Life Calculations

To find the remaining amount of a substance after a specific time period, use the decay formula: N(t) = N₀ * (1/2)^(t/T). In this equation, N(t) is the remaining amount after time t, N₀ is the initial amount, and T represents the time it takes for half of the substance to decay.

For example, if you start with 200 grams of a material and the decay time is 5 hours, the amount remaining after 10 hours would be calculated as follows:

Step 1: Use the formula with N₀ = 200, T = 5, and t = 10:

N(10) = 200 * (1/2)^(10/5) = 200 * (1/2)^2 = 200 * 0.25 = 50 grams

This means after 10 hours, 50 grams of the original 200 grams will remain. By applying this formula to different scenarios, you can solve for the remaining substance at any given time based on its half-life.