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. It represents growth or decay processes.

Front

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

Back

The base 'b' indicates the growth or decay factor. If b > 1, the function represents exponential growth; if 0 < b < 1, it represents exponential decay.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time period.

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What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time period.

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify exponential growth from a graph?

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Exponential growth is identified by a curve that rises steeply as x increases, indicating that the function's value increases rapidly.

Tags

CCSS.HSF-IF.C.7E

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How do you identify exponential decay from a graph?

Back

Exponential decay is identified by a curve that falls steeply as x increases, indicating that the function's value decreases rapidly.

Tags

CCSS.HSF-IF.C.7E

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What is the starting amount in the function f(t) = 300(1.05)^t?

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The starting amount is 300.

Tags

CCSS.HSF.LE.B.5

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Write the equation for a population that starts at 4 and grows at a rate of 67% per time period.

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The equation is y = 4(1.67)^x.

Tags

CCSS.HSF.LE.A.2

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What does the term 'growth rate' mean in the context of exponential functions?

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The growth rate is the percentage increase in the quantity per time period, expressed as a decimal in the function.

Tags

CCSS.HSF-IF.C.8B

Front

If a quantity decreases by 25% each year, what is the decay factor?

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The decay factor is 0.75, since 1 - 0.25 = 0.75.

Tags

CCSS.HSF-LE.A.1C