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Mathematics · Grade 12

Exponential and Logarithmic Models

Learners use exponential and logarithmic functions as modeling tools: cooling toward room temperature, logistic growth with a carrying capacity, straightening exponential data with a semi-log plot, and logarithmic scales such as pH and decibels. Throughout, they compare models and explain which assumptions each one makes.

  • 4 lessons
  • About 130 minutes
  • Exponential and logarithmic models check: 10 questions
  • Ways to answer: fill in the blanks, choose an answer, highlight a text, match pairs, type a number and put in order
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What learners will discover

  • Model situations that approach a limiting value, such as cooling y = C + A·b^t^, and solve for time using logarithms.
  • Interpret logistic growth models: initial value, carrying capacity and the time of fastest growth.
  • Linearize exponential data with logarithms and recover an exponential model from a semi-log line.
  • Use logarithmic scales (pH, decibels) to compare quantities that span many powers of ten.

Lessons

  1. Cooling toward the surroundings 6 steps4 practiceabout 34 min
  2. Logistic growth 6 steps3 practiceabout 30 min
  3. Straightening data with logarithms 6 steps4 practiceabout 32 min
  4. Logarithmic scales 6 steps3 practiceabout 34 min
  5. Exponential and logarithmic models check 10 questions at the end

Keep exploring

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