EXPONENTIALS & LOGARITHMS · TEXTBOOK LESSON
This chapter develops the mathematical ideas behind Growth and decay. The emphasis is on understanding the meaning of the mathematics, representing it clearly, choosing an efficient method, and checking that an answer is reasonable.
Learning objectives
By the end of this lesson, you should be able to:
- Explain the meaning of Growth and decay using correct mathematical language.
- Choose and apply an appropriate method accurately.
- Show working in a logical sequence and communicate the final answer clearly.
- Check results using estimation, inverse operations, substitution, units, or another suitable strategy.
1. Key vocabulary and definition
Definition
In mathematics, Growth and decay is studied by identifying the quantities or relationships involved, representing them precisely, and applying valid rules to reach a justified conclusion.
Growth and decaymethodreasoningcheck
2. Essential facts and rules
These are the facts you should know before attempting the worked example.
Key mathematical facts
- Write each step so another learner can follow the reasoning.
- Keep symbols, signs, labels and units consistent throughout a solution.
- A correct method is as important as a correct final answer.
3. Standard method
A reliable method helps prevent errors and makes your reasoning easy to follow.
1
Identify exactly what the question gives and what it asks you to find.
2
Represent the information using numbers, symbols, a diagram, a table or a graph as appropriate.
3
Select the relevant mathematical rule or relationship.
4
Carry out the calculation one step at a time.
5
Check the result and state the answer in context.
4. Worked example
Worked example
Construct a simple example that uses Growth and decay, solve it clearly, and explain why each step is valid.
1
List the known information and the unknown quantity.
2
Choose the mathematical representation or rule that connects them.
3
Apply the rule carefully and simplify.
4
Check the result using a second method where possible.
5. Common mistakes
Watch out for these
- Starting calculations before deciding what the question is asking.
- Skipping important steps or changing notation midway through a solution.
- Accepting an answer without checking whether its size, sign or unit is sensible.
6. Video lesson
This topic is ready for a matching video lesson. The written textbook lesson is fully available now; additional videos can be added to the same lesson template.
7. Practice exercise
Complete these without looking at the answers first.
- State the key rule or idea used in Growth and decay.
- Solve a straightforward example and show every step.
- Solve a second example that requires one extra step of reasoning.
- Write a short explanation of how you would check your answer.
- Create your own problem on this topic and solve it.
Show answers
- Answers depend on the examples chosen; the rule and working must be mathematically valid.
- The solution should show a clear sequence from the given information to the result.
- A valid check should confirm the same result or show that the answer is reasonable.
8. Chapter summary
- Understand the underlying idea before memorising a procedure.
- Use precise mathematical notation and show a logical method.
- Always check the final result.