Blitz - Practice - Key Factors of 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 it mean for a function to exhibit exponential growth?

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Exponential growth occurs when a quantity increases by a consistent percentage over equal time intervals, resulting in a rapid increase.

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What does it mean for a function to exhibit exponential decay?

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Exponential decay occurs when a quantity decreases by a consistent percentage over equal time intervals, leading to a rapid decrease.

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How do you identify the growth rate in an exponential function?

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The growth rate can be identified from the function f(x) = a(1 + r)^x, where 'r' is the growth rate expressed as a decimal.

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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 point where x = 0, which is (0, a).

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If a culture of bacteria decreases by 30% each year, what is the decay factor?

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The decay factor is 0.7, which represents the remaining percentage of the culture after each year.

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How do you write an exponential decay function for a starting amount of 5000 cells decreasing by 30% each year?

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The function is y = 5000(0.7)^x.

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What is the formula for exponential growth?

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The formula for exponential growth is f(x) = a(1 + r)^x, where 'a' is the initial amount and 'r' is the growth rate.

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How do you convert a percentage growth rate to a decimal for use in an exponential function?

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To convert a percentage growth rate to a decimal, divide the percentage by 100.

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What is the significance of the base in an exponential function?

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