Half-life and population doubling

Learning Objectives Define 'half-life' and 'population doubling' in their own words. Calculate the amount of a substance remaining after one half-life. Calculate the population size after one doubling period. Describe the pattern of change (halving or doubling) over multiple time periods. Solve simple word problems involving half-life and population doubling. Explain real-world examples where half-life and population doubling occur. Have you ever wondered how long it takes for a medicine to leave your body, or how quickly bacteria can multiply? 🦠 These are examples of amazing patterns in nature! In this lesson, we'll explore two fascinating ways things change over time: 'half-life' and 'population doubling'. You'll learn ho...

TermDefinitionExample Half-lifeThe amount of time it takes for a quantity of something to reduce to half of its original amount.If a medicine has a half-life of 4 hours, and you start with 100mg, after 4 hours you will have 50mg left. Population DoublingThe amount of time it takes for a population or quantity to grow to twice its original amount.If a bacteria population doubles every 30 minutes, and you start with 100 bacteria, after 30 minutes you will have 200 bacteria. Initial AmountThe starting quantity or number of something before any change occurs.If you start with 200 grams of a substance, 200 grams is the initial amount. Final AmountThe quantity or number of something after a certain amount of time or after changes have occurred.If you started with 100 bacteria and they doubled t...

Calculating Amount After One Half-life $A_{new} = A_{initial} \div 2$ To find the new amount after one half-life period, you take the initial amount and divide it by 2. Calculating Amount After One Doubling Period $A_{new} = A_{initial} \times 2$ To find the new amount after one population doubling period, you take the initial amount and multiply it by 2. Pattern for Multiple Half-lives To find the amount after 'n' half-lives, you divide the initial amount by 2, 'n' separate times. Each time a half-life period passes, the current amount is cut in half. So, for two half-lives, you divide by 2, then divide that result by 2 again. Pattern for Multiple Doubling Periods To find the amount after 'n' doubling periods, you multiply the ini...