EOC Category 5 - Exponential Functions

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What is an exponential function?

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An exponential function is a mathematical function of the form f(x) = a(b)^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

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What does the base of an exponential function represent?

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The base of an exponential function represents the growth (if greater than 1) or decay (if between 0 and 1) factor of the function.

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How do you identify exponential decay?

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Exponential decay occurs when the base of the exponential function is between 0 and 1, indicating a decrease in value over time.

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What is the y-intercept of an exponential function?

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The y-intercept of an exponential function f(x) = a(b)^x is the value of 'a', which represents the initial value when x = 0.

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What is the growth factor in an exponential function?

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The growth factor is the base 'b' in the function f(x) = a(b)^x, which indicates how much the function increases for each unit increase in x.

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How do you write an exponential function for a population that doubles every day?

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The function can be written as f(x) = a(2)^x, where 'a' is the initial population.

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What is the formula for exponential decay?

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The formula for exponential decay is f(x) = a(1 - r)^x, where 'r' is the decay rate.

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How do you determine the decay rate from an exponential function?

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The decay rate can be determined from the function f(x) = a(b)^x by calculating r = 1 - b, where b is the base.

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What is the difference between exponential growth and linear growth?

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Exponential growth increases at a rate proportional to its current value, while linear growth increases by a constant amount.

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How can you identify the greatest growth factor among multiple exponential functions?

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The greatest growth factor can be identified by comparing the bases of the functions; the function with the largest base indicates the greatest growth.