Writing Exponential Equations

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What is an exponential function?

Back

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

Front

How do you write an exponential function based on a real-world scenario?

Back

To write an exponential function based on a real-world scenario, identify the initial amount (a) and the growth/decay factor (b), then use the form y = a * b^x, where x represents time or another variable.

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What is the y-intercept of an exponential function?

Back

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 determine the growth/decay factor from an exponential function?

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The growth/decay factor is the base b in the exponential function f(x) = a * b^x. It indicates how much the quantity increases (if b > 1) or decreases (if 0 < b < 1) for each unit increase in x.

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What is the general form of an exponential growth equation?

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The general form of an exponential growth equation is y = a * b^x, where a is the initial amount and b is the growth factor (b > 1).

Front

What is the general form of an exponential decay equation?

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The general form of an exponential decay equation is y = a * b^x, where a is the initial amount and b is the decay factor (0 < b < 1).

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How can you identify an exponential function from a graph?

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An exponential function can be identified from a graph by its characteristic curve, which rises or falls rapidly and approaches the x-axis but never touches it (asymptotic behavior).

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What is the significance of the initial value in an exponential function?

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The initial value in an exponential function represents the starting amount before any growth or decay occurs, and it is the y-intercept of the function.

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How do you convert a real-world scenario into an exponential equation?

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To convert a real-world scenario into an exponential equation, identify the initial amount, determine the growth or decay factor, and express it in the form y = a * b^x.