Exploring Exponential Functions

This video tutorial introduces exponential functions, explaining their form and characteristics. It covers the roles of 'a' as the y-intercept and 'b' as the factor, and demonstrates how to create input-output tables. The tutorial also discusses exponential growth and decay, showing how to identify them based on the factor 'b'. Examples are provided to illustrate these concepts, and the video concludes with a summary and resources for further learning.

What defines an exponential function?

• A function whose exponent is a variable

• A function with a constant exponent

• A function that cannot be graphed

• A function that only contains integers

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What does the 'a' value in an exponential function represent?

• The rate of growth or decay

• The y-intercept

• The x-intercept

• The slope of the graph

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In the function y = 5 * 2^x, what is the y-intercept?

• 5

• 0

• 10

• 2

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What does the 'b' value in an exponential function indicate?

• The y-intercept

• The x-intercept

• The factor or rate of growth/decay

• The maximum value of the function

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What is the y-intercept of the function f(x) = 144 * (1/2)^x?

• 0

• 144

• 1/2

• 72

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For the function y = 144 * (1/2)^x, what is the factor?

• 144

• 1/2

• 2

• 0

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What pattern do you observe in the output values of a function showing exponential decay?

• The output values increase

• The output values decrease

• The output values remain constant

• The output values alternate between increasing and decreasing

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How do you identify exponential growth in a function?

• When 'b' value equals 1

• When 'b' value is greater than 1

• When 'b' value is less than 0

• When 'b' value is between 0 and 1

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Which of the following functions exhibits exponential growth?

• y = 200 * (1/2)^x

• y = 50 * (1.5)^x

• y = 100 * (0.99)^x

• y = 3 * (2/3)^x

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CCSS.HSF.LE.A.1

Which factor indicates exponential decay?

• 2/3

• 5

• 1

• 2

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