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Exponential Decay and Half-life
For decay y=y0e(-kt); half-life satisfies e(-kT)=12.
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Exponential Decay and Half-life
What is it?
For decay y=y0e(-kt); half-life satisfies e(-kT)=12.
In simple words
- For decay y=y0e(-kt); half-life satisfies e(-kT)=12.
- Worked pattern: If half-life is 5 years, k=ln2/5.
- Final check: domain, sign, notation, units, and reasonableness.
Important terms
Exponential decay and half-life: For decay y=y0e^(-kt); half-life satisfies e^(-kT)=12.
What you should learn
- State the rule for exponential decay and half-life.
- Solve a exponential decay and half-life problem step by step.
- Check the result, restrictions, notation, and units.
Recommended for Class 12
Full school-level explanation
For decay y=y0e(-kt); half-life satisfies e(-kT)=12.
CONCEPT AND RULE
For decay y=y0e(-kt); half-life satisfies e(-kT)=12.
METHOD
For exponential decay and half-life, identify the given information and required result. Select the matching definition or formula, state its conditions, substitute carefully, simplify one line at a time, and check.
WORKED EXAMPLE
If half-life is 5 years, k=ln2/5.
COMMON MISTAKE
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
How to solve exponential decay and half-life
How it works
- Identify the mathematical objects, givens, restrictions, and required result.
- Choose and write the relevant definition, theorem, or formula.
- Substitute with brackets and carry out one justified step per line.
- Simplify, state the final answer clearly, and verify it in the original setting.
Remember
- Exponential decay and half-life
- rule
- worked example
- worked example
How the ideas connect
Worked example: If half-life is 5 years, k=ln2/5.
Deeper understanding
Go beyond memorising Exponential Decay and Half-life. Connect the definition to reasons, relationships, exceptions, and exam wording.
How the ideas connect
Worked example: If half-life is 5 years, k=ln2/5.
Common mistakes
Exam focus
Core Idea
Rule / Formula
Method
Worked Example
Exam focus
Quick revision
- Exponential decay and half-life
- rule
- worked example
- Exponential decay and half-life: For decay y=y0e^(-kt); half-life satisfies e^(-kT)=12.
- CONCEPT AND RULE: For decay y=y0e^(-kt); half-life satisfies e^(-kT)=12.
- METHOD: For exponential decay and half-life, identify the given information and required result. Select the
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
For long answers on Exponential Decay and Half-life: define clearly → explain the main parts → give one example → state one exam caution.
Exam Focus
Exam Focus
Important points
- Exponential decay and half-life
- rule
- worked example
- Exponential decay and half-life: For decay y=y0e^(-kt); half-life satisfies e^(-kT)=12.
Important formulas
- Exponential decay and half-life
- rule
- worked example
Common exam traps
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- A matching-looking formula is not valid until its conditions and domain have been checked.
Long question structure
Definition → key parts → example → exam caution
Common Mistakes
Common Mistakes
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
- Mistake
A matching-looking formula is not valid until its conditions and domain have been checked.
- Mistake
Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all domain or interval conditions.
Revision Zone
60-Second Revision
Quick cues from this topic — use them for last-minute revision.
Exponential decay and half-life
rule
worked example
Exponential decay and half-life: For decay y=y0e^(-kt); half-life satisfies e^(-kT)=12.
For decay y=y0e(-kt); half-life satisfies e(-kT)=12.
- Definition
- For decay y=y0e(-kt); half-life satisfies e(-kT)=12.
- Critical warning
- Write the governing rule before substitution, keep brackets and signs visible, and check that the answer satisfies all d
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Exam Practice
Define
Q1. Define Exponential Decay and Half-life.
Explain
Q2. Explain: CONCEPT AND RULE.
Example
Q3. Give one clear example of Exponential Decay and Half-life and say why it fits.
Mistake
Q4. State one common mistake students make about Exponential Decay and Half-life.
Exam note
Q5. Write a short exam note on Exponential Decay and Half-life: definition, two points, one example.
Sources & References
School-standard facts for Matric and Intermediate. Original explanations — not copied from textbooks.