Interpreting Exponential Functions Using Function Notation Task

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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. It describes growth or decay processes.

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What does the notation f(d) represent in the context of functions?

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f(d) represents the value of the function f at a specific input d. It indicates how the output of the function changes based on the input value.

Tags

CCSS.HSF.IF.A.2

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What is the initial value in an exponential function?

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The initial value is the value of the function when the input is zero, often represented as f(0). It indicates the starting point of the function.

Tags

CCSS.HSF.LE.B.5

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How do you interpret f(4.5) in the context of a flu epidemic?

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f(4.5) represents the number of people with the flu after 4.5 days since the epidemic began.

Tags

CCSS.HSF.IF.B.4

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What does the base of an exponential function indicate?

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The base indicates the growth or decay factor. If the base is greater than 1, the function represents growth; if it is between 0 and 1, it represents decay.

Tags

CCSS.HSF-IF.C.8B

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How can you find the value of f(t) for a specific t in an exponential function?

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To find f(t), substitute the value of t into the function's equation and calculate the result.

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What does it mean if f(t) = 1500 in the context of a flu epidemic?

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It means that after a certain number of days, the number of people with the flu reached 1500.

Tags

CCSS.HSF.LE.B.5

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

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The coefficient (the constant 'a' in f(x) = a * b^x) represents the initial amount or starting value of the function.

Tags

CCSS.HSF.LE.B.5

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How do you determine the rate of growth in an exponential function?

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The rate of growth is determined by the base of the exponential function. For example, in f(d) = 50 * (3/2)^d, the growth rate is (3/2) per day.

Tags

CCSS.HSF-IF.C.8B

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What does it mean for a function to be increasing exponentially?

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A function is increasing exponentially if its output values grow at an increasing rate as the input values increase.