Modeling 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(t) = a(b)^t, where 'a' is a constant, 'b' is the base (a positive real number), and 't' is the exponent. It represents growth or decay processes.

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

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In an exponential function, 'a' represents the initial value or y-intercept of the function.

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

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The base 'b' in an exponential function indicates the growth (b > 1) or decay (0 < b < 1) factor of the function.

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

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The initial value can be identified as the coefficient 'a' in the function f(t) = a(b)^t.

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What is the general form of an exponential growth function?

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The general form of an exponential growth function is f(t) = a(1 + r)^t, where 'r' is the growth rate.

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What is the general form of an exponential decay function?

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The general form of an exponential decay function is f(t) = a(1 - r)^t, where 'r' is the decay rate.

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What type of pattern do exponential functions exhibit?

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Exponential functions exhibit a pattern where they multiply or divide by the same number (the base) for each unit increase in 't'.

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What is the difference between linear and exponential functions?

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Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant factor.

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In the equation y = mx + b, what does 'b' represent?

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'b' represents the y-intercept or initial value of the linear function.

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How can you graph an exponential function?

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To graph an exponential function, plot points for various values of 't' and connect them to show the rapid increase or decrease.