Exponential Functions - WORD PROBLEMS

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What is an exponential function?

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An exponential function is a mathematical function of the form y = a(b^x), where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent. It represents growth or decay processes.

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What does exponential growth mean?

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

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CCSS.HSF-IF.C.8B

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What does exponential decay mean?

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

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CCSS.HSF-IF.C.8B

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How do you identify exponential growth from a graph?

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Exponential growth graphs rise sharply and curve upwards, indicating that the rate of increase accelerates over time.

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CCSS.HSF-IF.C.7E

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How do you identify exponential decay from a graph?

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Exponential decay graphs fall sharply and curve downwards, indicating that the rate of decrease accelerates over time.

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CCSS.HSF-IF.C.7E

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What is the general form of an exponential decay equation?

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The general form is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

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CCSS.HSF-IF.C.8B

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What is the general form of an exponential growth equation?

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The general form is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

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If a population of bacteria doubles every hour, what type of function does this represent?

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This represents exponential growth.

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CCSS.HSF-LE.A.1A

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If a car's value decreases by 15% each year, what type of function does this represent?

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This represents exponential decay.

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What is the initial value in an exponential function?

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The initial value is the starting amount before any growth or decay occurs, represented by 'a' in the equation.