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Mathematics · Grade 9

Exponents and Exponential Growth

Learners derive the laws of integer exponents from the meaning of repeated multiplication (including zero and negative exponents), then build exponential functions y = a·b^x^ and interpret their initial value, growth or decay factor and percent rate. They contrast constant differences with constant ratios, see why exponential growth eventually overtakes any linear growth, and model compound interest, depreciation, half-life and geometric sequences.

  • 4 lessons
  • About 125 minutes
  • Exponents and exponential growth check: 11 questions
  • Ways to answer: choose an answer, type a fraction, match pairs, type a number, sort into groups and true or false
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What learners will discover

  • Derive and apply the laws of integer exponents, including zero and negative exponents, and compute with scientific notation.
  • Write and interpret exponential functions y = a·b^x^ from descriptions, tables and graphs, identifying the initial value, growth or decay factor and percent rate.
  • Distinguish linear from exponential relationships by constant differences versus constant ratios, and explain why exponential growth eventually exceeds linear growth.
  • Model situations with exponential growth and decay (compound interest, depreciation, half-life) and with geometric sequences, and interpret the results.

Lessons

  1. Exponent laws from the meaning of exponents 8 steps6 practiceabout 30 min
  2. Exponential functions 7 steps4 practiceabout 30 min
  3. Linear versus exponential 7 steps4 practiceabout 32 min
  4. Modeling growth and decay 8 steps4 practiceabout 33 min
  5. Exponents and exponential growth check 11 questions at the end

Keep exploring

More 9th grade math

Guide for grown-ups