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Course 1, Unit 5 - Exponential Functions

Overview
In the Exponential Functions unit, students analyze situations that can be modeled well by rules of the form y = a(b)x. They construct and use data tables, graphs, and equations in the form y = a(b)x to describe and solve problems about exponential relationships such as population growth, investment of money, and decay of medicines and radioactive materials. Some of these topics are often introduced in middle school math courses. Encourage your student to recall these ideas. Some of these questions may be helpful. They also use exponent rules to simplify exponential and radical expressions.

Key Ideas from Course 1, Unit 5

  • Exponential growth or decay relationship: In the rule y = a(b)x, b is the constant growth or decay factor. In tables where x is increasing in uniform steps, the ratios of succeeding y values will always be b. If b is greater than 1, the pattern will be exponential growth; if b is between 0 and 1, the pattern will be exponential decay. The value of a indicates the y-intercept (0, a) of the graph of the relationship.

    For example, y = 4(0.5)x represents an exponential decay relationship between x and y, where the initial value of y (when x = 0) is 4, and the y values decrease by 50% for each increase of 1 in x values. The table would begin as follows:

    x
    0
    1
    2
    3
    y
    4
    2
    1
    0.5
  • NOW-NEXT equations: Since exponential growth involves repeated multiplication by a constant factor, those patterns can be represented by equations in the general form NEXT = b * NOW, starting at a. For example, the pattern of change in a population growing at a rate of 20% per year from a base of 5 million in the year 2000 can be expressed as NEXT = 1.20NOW, starting at 5. (See pages 291-301.)

    Year
    2000
    2001
    2002
    2003
    Population (in millions)
    5
    6
    7.2
    8.64
  • Rewriting exponential expressions: See the unit summary below for the exponent rules. Practice using these rules is distributed throughout the Review tasks in subsequent units. (See pages 304-306, 332-337.)

    Example:

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