Half-life
Master Half-life in Grade 10 math. The half-life of a substance is the amount of time it takes for one-half of that substance to decay.. Practice with Saxon Algebra 2 examples.
Key Concepts
The half life of a substance is the amount of time it takes for one half of that substance to decay. This is a classic application of exponential decay, where the decay factor 'b' is calculated based on the fact that the quantity becomes 0.5 of its original amount after one half life period. The general model is $y=a(b)^x$.
An element has a half life of 58 minutes. To find the decay model $y = b^x$, we solve $0.5 = b^{58}$. The base is $b = \sqrt[58]{0.5} \approx 0.988$. The model is $y = (0.988)^x$. Carbon 14 has a half life of 5730 years. A 10 kg mass after 9000 years is $y = 10(\sqrt[5730]{0.5})^{9000}$, leaving approximately 3.36 kg.
Think of a potion losing its magic. The half life is the time it takes for half its power to disappear. After one half life, it's at 50% strength. After another, it loses half of that , dropping to 25% strength.
Common Questions
What is Half-life?
The half-life of a substance is the amount of time it takes for one-half of that substance to decay. This is a classic application of exponential decay, where the decay factor 'b' is calculated based on the fact that the quantity becomes 0.5 of its original amount after one half-life period. The...
How do you apply Half-life in practice?
An element has a half-life of 58 minutes. To find the decay model , we solve . The base is . The model is . Carbon-14 has a half-life of 5730 years. A 10 kg mass after 9000 years is , leaving approximately 3.36 kg.
Why is Half-life important for Grade 10 students?
Half-life is the time it takes for half of a substance to disappear. Think of it like a video game power-up that wears off: after a set time, its strength is cut in half. Then after that same amount of time again, its remaining strength is cut in half again! It's an example of exponential decay....