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.

Front

What does the base in an exponential function represent?

Back

The base in an exponential function represents the growth (if greater than 1) or decay (if between 0 and 1) factor of the function.

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How do you write an exponential decay function?

Back

An exponential decay function can be written as f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Front

What is the decay rate in the function f(x) = 500(0.9)^x?

Back

The decay rate is 10%, since 1 - 0.9 = 0.1 or 10%.

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How do you convert a percentage decay rate to a decimal for an exponential function?

Back

To convert a percentage decay rate to a decimal, divide the percentage by 100. For example, 12% becomes 0.12.

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What does the initial value 'a' represent in an exponential function?

Back

The initial value 'a' represents the starting amount or value of the quantity being modeled.

Front

Write an exponential function for a population of 2000 that decreases by 25% each year.

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f(t) = 2000(0.75)^t.

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What does the term 'growth factor' mean in an exponential function?

Back

The growth factor is the base of the exponential function when it is greater than 1, indicating how much the quantity increases.

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If a function is modeled as f(x) = 100(1.05)^x, what does 1.05 represent?

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1.05 represents a 5% growth rate.

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How do you determine the percentage growth or decay from an exponential function?

Back

To determine the percentage growth or decay, subtract 1 from the base of the function and multiply by 100. For example, for f(x) = 300(1.06)^x, the growth rate is (1.06 - 1) * 100 = 6%.