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4
x+1=5.
Class 12 · English Medium · Cambridge · Mathematics
Number, fractions, decimals and percentages
Use exponential equations and logarithms to compare changing quantities.
About this lesson and its coverage
Original Kidemy Class 12 progression. This level has its own text, examples and questions. Curriculum versions share the progression; complete board-specific coverage still needs specification matching and additional material.
Learn the idea
An exponential model has a quantity multiplied by a fixed factor per interval. Solving for time often requires logarithms. A model parameter describes the chosen mathematical relationship; it is not evidence that a real rate remains fixed indefinitely.
Worked example
For V=600(1.08)^t, reaching1200 gives t=ln2/ln1.08. The first whole-number period reaching the target is the next integer above the continuous solution.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
Show your working on paper. Check your answer, then choose Next.
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3
Natural log reverses the exponential.
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1.44
1.2².
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x=ln7/2.
Take logs and divide by 2.
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A real-valued time can fall between observation dates; the first annual check reaching it may be later.
Explain the timing convention.
Progress and browser storage
Notebook challenge, sources and further study
Apply the idea
Compare two hypothetical exponential models and state where extrapolation could fail.
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- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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