Writing 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 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.

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How do you write an exponential decay function?

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An exponential decay function can be written as f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

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What is the formula for exponential growth?

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The formula for exponential growth is f(t) = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

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If a quantity decreases by 30% each year, what is the decay factor?

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The decay factor is 0.7, which means you multiply the initial amount by 0.7 each year.

Tags

CCSS.HSF-LE.A.1C

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How do you model the depreciation of a car's value?

Back

To model depreciation, use the formula V(t) = a(1 - r)^t, where 'a' is the initial value, 'r' is the depreciation rate, and 't' is time in years.

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What does the y-intercept represent in an exponential function?

Back

The y-intercept represents the initial value of the function when x = 0.

Tags

CCSS.HSF-IF.C.7E

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How do you find the number of cells after a certain time if they triple every hour?

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Use the function f(h) = a(3)^h, where 'a' is the initial number of cells and 'h' is the number of hours.

Tags

CCSS.HSF.LE.A.2

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What is the difference between exponential growth and exponential decay?

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Exponential growth increases over time, while exponential decay decreases over time.

Tags

CCSS.HSF-IF.C.8B

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How can you identify an increasing exponential function?

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An increasing exponential function has a base greater than 1, which causes the function to rise as x increases.

Tags

CCSS.HSF-IF.C.7E

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What is the general form of an exponential function?

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The general form of an exponential function is f(x) = a(b)^x, where 'a' is a constant and 'b' is the base.