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Exponential Functions: Growth and Decay

Learn how to write and evaluate exponential expressions to model growth and decay situations. Understand the vocabulary of exponential functions, such as base, asymptote, exponential growth, and exponential decay.

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Exponential Functions: Growth and Decay

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  1. Exponential Functions, Growth and Decay 9-2 Warm Up Lesson Presentation Lesson Quiz Holt McDougal Algebra 2 Holt Algebra 2

  2. Warm Up Evaluate. 1. 100(1.08)20 2. 100(0.95)25 ≈ 466.1 ≈ 27.74

  3. Essential Question How do you write and evaluate exponential expressions to model growth and decay situations?

  4. Vocabulary exponential function base asymptote exponential growth exponential decay

  5. Growth that doubles every year can be modeled by using a function with a variable as an exponent. This function is known as an exponential function. The parent exponential function is f(x) = bx, where the baseb is a constant and the exponent x is the independent variable.

  6. The graph of the parent function f(x) = 2xis shown. The domain is all real numbers and the range is {y|y > 0}.

  7. Notice as the x-values decrease, the graph of the function gets closer and closer to the x-axis. The function never reaches the x-axis because the value of 2xcannot be zero. In this case, the x-axis is an asymptote. An asymptote is a line that a graphed function approaches as the value of x gets very large or very small.

  8. A function of the form f(x) = abx, with a > 0 and b > 1, is an exponential growth function, which increases as x increases. When 0 < b < 1, the function is called an exponential decay function, which decreases as x increases.

  9. The base , ,is less than 1. This is an exponential decay function. Example 1A: Graphing Exponential Functions Tell whether the function shows growth or decay. Then graph. Step 1 Find the value of the base.

  10. Example 1A Continued Step 2 Graph the function by using a table of values.

  11. Example 1B: Graphing Exponential Functions Tell whether the function shows growth or decay. Then graph. g(x) = 100(1.05)x Step 1 Find the value of the base. The base, 1.05, is greater than 1. This is an exponential growth function. g(x) = 100(1.05)x

  12. Example 1B Continued Step 2 Graph the function by using a graphing calculator.

  13. Check It Out! Example 1 Tell whether the function p(x) = 5(1.2x) shows growth or decay. Then graph. Step 1 Find the value of the base. p(x) = 5(1.2x) The base , 1.2, is greater than 1. This is an exponential growth function.

  14. Check It Out! Example 1 Continued Step 2 Graph the function by using a table of values.

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