6.1 Classwork (Writing Exponential functions)

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What is an exponential function?

Back

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.

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What does the base of an exponential function represent?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth; if the base is between 0 and 1, it represents exponential decay.

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How do you identify the starting term in an exponential function?

Back

The starting term in an exponential function f(x) = a(b)^x is represented by 'a'. It is the value of the function when x = 0.

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What is the recursive formula for an exponential sequence?

Back

The recursive formula for an exponential sequence can be expressed as a_n = r * a_{n-1}, where 'r' is the common ratio.

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Write the exponential function for a sequence with a starting term of 16 and a common ratio of 0.5.

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f(x) = 16(0.5)^x.

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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(b)^x, where 0 < b < 1.

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How do you convert a table of values into an exponential function?

Back

To convert a table of values into an exponential function, identify the starting term and the common ratio, then use the form f(x) = a(b)^x.

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

Back

The exponent in an exponential function indicates the number of times the base is multiplied by itself, affecting the growth or decay rate.

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How can you determine the equation of an exponential function from a graph?

Back

To determine the equation of an exponential function from a graph, identify key points, especially the y-intercept and the growth/decay rate, then use the form f(x) = a(b)^x.

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What is the difference between exponential growth and exponential decay?

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Exponential growth occurs when the base of the function is greater than 1, leading to increasing values. Exponential decay occurs when the base is between 0 and 1, leading to decreasing values.