Writing Exponential Functions from Word Problems

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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 initial value (y-intercept) represent in an exponential function?

Back

The initial value (or y-intercept) represents the value of the function when x = 0. It indicates the starting amount before any growth or decay occurs.

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How do you identify exponential growth in a function?

Back

Exponential growth occurs when the base 'b' in the function f(x) = a(b)^x is greater than 1.

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How do you identify exponential decay in a function?

Back

Exponential decay occurs when the base 'b' in the function f(x) = a(b)^x is between 0 and 1.

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What is the formula for exponential growth?

Back

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.

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What is the formula for exponential decay?

Back

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

Front

How do you write an exponential function from a word problem?

Back

Identify the initial value, the rate of growth or decay, and the time variable. Use the formula f(t) = a(1 ± r)^t to write the function.

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

Back

The rate of increase refers to the percentage by which the initial value grows over a specific period of time.

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

Back

The rate of decrease refers to the percentage by which the initial value declines over a specific period of time.

Front

If a function is modeled by f(x) = 500(0.8)^x, what does 0.8 represent?

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In this function, 0.8 represents the decay factor, indicating that the quantity decreases by 20% each time period.