Exponential Functions DOL

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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 determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

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What is the y-intercept of an exponential function?

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The y-intercept of an exponential function is the value of the function when x = 0, which is equal to the constant 'a' in the function f(x) = a * b^x.

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How do you find the initial value in an exponential function?

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The initial value in an exponential function is the value of the function at time t = 0, which corresponds to the y-intercept.

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What is the formula for exponential decay?

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The formula for exponential decay can be expressed as V(t) = V_0 * (1 - r)^t, where V_0 is the initial value, r is the decay rate, and t is time.

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What is the formula for exponential growth?

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The formula for exponential growth can be expressed as V(t) = V_0 * (1 + r)^t, where V_0 is the initial value, r is the growth rate, and t is time.

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How do you model a situation with exponential decay?

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To model a situation with exponential decay, identify the initial value and the decay rate, then use the formula V(t) = V_0 * (1 - r)^t.

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What is the significance of the decay rate in an exponential decay function?

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The decay rate indicates the percentage by which the quantity decreases each time period. A higher decay rate results in a faster decrease.

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What is the significance of the growth rate in an exponential growth function?

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The growth rate indicates the percentage by which the quantity increases each time period. A higher growth rate results in a faster increase.

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How can you determine if a function represents growth or decay?

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You can determine if a function represents growth or decay by examining the base of the exponential function: if the base is greater than 1, it represents growth; if the base is between 0 and 1, it represents decay.