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Understanding Exponential Functions: Growth and Decay Analysis

This lesson focuses on evaluating expressions for a given value and explores the concepts of exponential growth and decay in mathematical functions. Through hands-on examples and essential questions, students will learn to distinguish between linear, quadratic, and exponential functions. The activities involve calculating bacteria growth, assessing changes in expressions, and identifying function types. This foundational knowledge will aid students in understanding real-world applications of exponential functions. Assignment and classwork questions reinforce learning outcomes.

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Understanding Exponential Functions: Growth and Decay Analysis

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  1. Warm-Up: January 30, 2013 • Evaluate each expression for x=2 • x5 • 5x • 5-x

  2. Due: Page 358 #15-24, 26, 30, 36-41 16) 1.09 18) 0.98 20) 0.918 22) 1.0008 24) 32 26) 1024 30) 8100 36) a) 440 b) 1760 38) a) 132 b) 135,168 40) a) 675 b) 6075

  3. Homework Questions?

  4. Warm-Up: January 31, 2013 • A biologist places 100 bacteria in a petri dish. An hour later, there are 175 bacteria in the petri dish. • 1) What was the increase in bacteria? • 2) What is the growth rate of bacteria? • 3) How many bacteria would there be 24 hours after the biologist placed the first 100 bacteria into the petri dish?

  5. Exponential Functions Section 6.2

  6. Essential Question • Given a function, how can we tell if it is exponential growth, exponential decay, or not exponential?

  7. Exponential Function • Exponential Function: A function of the form f(x)=bxwhere the base, b, is a positive real number other than one.

  8. Example 1: Identify each as linear, quadratic, or exponential • f(x) = 3x-9 • g(x) = (x-3)(x+1) • h(x) = x(2-x) • j(x) = 3x – 24 • k(x) = 123x

  9. Growth vs. Decay for f(x)=a(b)x, a>0 • Exponential growth: b>1 and x>0 • Exponential decay: 0<b<1 and x>0 • If there is a negative in the exponent, take the reciprocal of b prior to testing for growth/decay.

  10. Example 2: Growth or Decay?

  11. Assignment • Page 367 #10-24 ALL

  12. Classwork Answers 10) linear 11) quadratic 12) exponential 13) exponential 14) exponential 15) quadratic • 16) growth • 17) growth • 18) decay • 19) decay • 20) decay • 21) decay • 22) decay • 23) decay • 24) decay

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