Day 06 - Exponential Growth/Decay - 08.25.14

Bell Ringer
  1. Simplify the following using exponent properties:

    1. (8p8)/81

    2. (16p8)/81

    3. (6p8)/81

    4. (16p8)/9

    5. none of the above

  2. Simplify the following radical expression:

    1. [square root(14x)] / 4

    2. [square root(7x)] / 4

    3. [square root(14x)] / 2

    4. [square root(7x)] / [2*square root(2)]

    5. none of the above

  3. Why is (23)(24) ≠ 47?

    1. Exponents should not be added together.

    2. The exponents should multiplied to get 12.

    3. The equation should have an equal sign.

    4. The two’s should not be multiplied together.

    5. none of the above

  4. Which would you rather have: Getting paid $500 a day for one month or starting with 1 penny and double it each day for one month? Explain your answer using math.

    1. $500 a day

    2. Doubling of a penny each day

  • Exponent Properties
    • Product of Powers
    • Power of a Power
    • Power of a Product
    • Quotient of Powers
    • Power of a Quotient
    • Zero Exponent
    • Negative Exponents
  • Radical Properties
    • Product of Square Roots
    • Quotient of Square Roots
    • Rationalizing the Denominator
    • Rational Exponents

    1. There is a well-known fable about a man from India who invented the game of chess, as a gift for his king. The king was so pleased with the game that he offered to grant the man any request within reason. The man asked for one grain of wheat to be placed on the first square of the chess board, two grains to be placed on the second square, four on the third, eight on the fourth, etc., doubling the number of grains of wheat each time, until all 64 squares on the board had been used. The king, thinking this to be a small request,  agreed. A chess board has 64 squares.
      • Create a table of values for 1 square up to 15 squares.
      • Graph the table of values.
      • Create an exponential function modeling the problem.
      • How many grains of wheat did the king have to place on the 64th square of the chess board?
    2. A scientist has discovered a new strain of bacteria.  The bacteria culture initially contained 1000 bacteria and the bacteria are doubling every half hour.
      • Create a table of values for the first 5 hours.
      • Graph the table of values.
      • Create an exponential function modeling the problem.
      • Using the graph, how many bacteria will there be at 45 minutes?

    • Exponential Growth and Decay Practice Problems
    • page 563 #1, 3, 7, 9, 10, 11-13, 18

    Exit Ticket

    1. A car sells for $16,000. If the rate of depreciation is 18% each year, what is the theoretical value of the car in 8 years?

      1. $3270.63

      2. $0.018

      3. $60,141.75

      4. $78,272.49

    2. In 2011, there were 185 rabbits in Central Park.  The population has increased by about 12% each year.  About how many rabbits were in Central Park in 2014?

      1. 260 rabbits

      2. 126 rabbits

      3. 0.32 rabbits

      4. 186 rabbits

    3. A sample of bacteria double every 3 hours. Choose the equation that best fits the model for the growth of bacteria.

      1. y = 2t/3

      2. y = 2t

      3. y = 2t

      4. y = t2

    Lesson Objective(s)
    • How does linear growth/decay differ from exponential growth/decay?
    • How can exponential growth/decay be modeled using mathematics?

    • N.RN.1  Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
    • N.RN.2  Rewrite expressions involving radicals and rational exponents using the properties of exponents.
    • A.CED.1 Create equations and inequalities in one variable and use them to solve problems.Include equations arising from linear and quadratic functions, and exponential functions.

    Mathematical Practice(s)
    • #2: Reason abstractly and quantitatively
      • Students will use concrete examples of numerical manipulation to examine closure of rational and irrational numbers. For example, students will use numeric examples of sums and products of rational numbers to generalize the closure of rational numbers under addition and multiplication.
    • #4: Model with mathematics
      • Students will create equations using rational or radical expressions to represent mathematical models of real-world situations like interest rates or depreciation.

    Summary of Concepts